check your battery connections and the connections on your alternator

Interesting! Was this phenomenon noticed in the oursuit of a specific problem?
If the anomaly occurred only while the engine was running I would suspect the meter was reacting to a "spike of reverse polarity voltage" (also called an AC spike) that was being superimpsed on the standing DC system voltage.
Spikes of this nature can be caused by the normal operation of a DC powered solenoid, relay, or motor. Motors and solenoids are surrounded by an electromagnetic field whenever they are energized (powered up). When the DC is interupted, this EMF field collapses and shrinks back into the progenitor coil. As this field shrinks back through the coil windings of the now de-energized solenoid or motor, a "secondary induced voltage" is created, which will flow out of the device with reversed polarity from the current that was feeding the coil when it was fed from the electrical system. The secondary induced voltage is usually quite high, it can go into the tens of thousands volts, but has almost no amperage power (if the progenitor coil is small).
In cases where the progenitor coil is large (meaning "significant amp draw"), such as PTO clutch on your lawn tractor (there you go, it's "on topic" now), or an air condition clutch, a diode may be added to the circuit by the OEM to shunt the secondary induced voltage to ground instead of letting the reverse polarity current possibly arc across the contacts of the switch controlling the power to the device.

This secondary induced voltage is not just a "single pulse" either. The collapsing field is energizing the coil too, though much less than when the coil was fed from the battery, and as this second field reaches its peak saturation moment, it too collapses, falling back through the coil and generating a "tertiary induced voltage", which by the way, matches the voltage of the electrical system now, and so on until all EMF activity ends.
This will show up on a very sensitive, analog type, DC volts scale as a wildly fluctuating needle (for a fleeting moment).
On an economy digital meter set to DC volts, you might see the polarity icon change from + to - and back a couple of times, along with the value trying to change, or just going blank as it can't react fast enough to show a value.

But it would seem that simply turning on the key switch would not provoke the operation of any solenoids, relays, or motors unless the operator moved a switch or control setting, or if there was an automatic process ongoing when the key is turned to ON.

Does this Jeep perhaps have a heater/AC fan that runs whenever the key is on (even if the manual fan switch is OFF). I know many GM products had cabin fans that ran on low speed whenever the key switch was on, even if the fan switch on the control console was in the OFF position.

Mownie, thanks for the explanation. In answer to whether a fan is running, no, no running fan. Also I was not working on another problem with it when I noticed this. It's not a daily driver, and I was just taking it for a short drive. Checked battery and it was down a little. Put it on slow charge (left battery connected) and that blip was showing on the meter on the battery charger. The key was off while this was going on. Is this detail a clue? I haven't torn the instrument panel out yet so haven't checked the guage out. Connections to the alternator are solid. Battery terminals are clean and tight.

My "insighter" must not be working.
Reading the opening post I get a different impression of the scene (probably my inference) than what I get out of the last post above.
In the opening post, I presumed this "wild fluctuation" was showing up on a hand held multimeter test instrument.
In the last post above, one might infer that the fluctuation is showing on the battery charger voltmeter.
But there is a line in the opening post "No other gauges are affected" that could imply the voltmeter is the onboard voltmeter in the vehicle instrument panel cluster.
How many voltmeters are exhibiting this behavior and where are they located?
If the fluctuation is occurring only when the battery charger is connected, the fluctuation might be originating from sporadic leakage of AC line voltage that gets past the rectifying bridge of the battery charger. If this was the case, the fluctuation would show up on any analog volt meter connected to the battery, whether it was on the charger per se, the instrument panel of the vehicle, or a hand held analog volt meter test instrument.

Or, it could be the battery charger voltage limiter chopping the current when the battery/system voltage rises to to the voltage limit setting of the charger.
If this is occurring, it could theoretically reach a point where this "cycling" of the voltage limiter would occur every "7 seconds or so" (or other interval) as the battery and the charger try to reach their own "Nirvana".

If it is in fact due to the battery charger voltage limiter action, AND the fluctuations occur only when the key is ON, the vehicle alternator may be the source of the spike.
With the key ON, the vehicle voltage regulator will energize the alternator FIELD windings whenever the vehicle electrical system voltage is less than the voltage limit setting of the regulator. Any change in the voltage level of the vehicle electrical system (either higher or lower change) will cause the alternator output windings (stator coils) emit a "pulse" of current, even though the alternator rotor is not spinning.
To visualize that, think of the non-moving alternator as if it was an ignition coil with the rotor (field) windings acting as the PRIMARY coil windings and the stator windings acting as the secondary windings. Any change of voltage level in the rotor windings will produce a pulse of induced current in the stator windings.
On an analog voltmeter the pulses would appear as a fluctuating spike similar to AC.

Try disconnecting various fuses (one at a time) and isolate the circuit.

It sounds like the old fashioned automotive clocks that would "wind up" every few minutes.

Thank you, gentlemen, for the replies. In answer to you, mownie, in the initial post, I meant that the fluctuations were from the dash mounted volt meter. The fluctuation occurs when motor is running and when the key only is on (not running) (Same type of fluctuation and interval which as I said is between 7 and 12 seconds. The fluctuation duration is only a fraction of a second - the brevity of a clock tick.)
Only discovered the battery charger meter was also affected when I checked the battery and discovered it was a little low and decided that if I was going to be checking things out I'd start with a fully charged battery.
The battery charger phenomenon occurs when the charger is on and connected to the Jeep and the ignition key is in the off position. The fluctuations occur on the dash gauge and the charger simultaneously.
Hope that clarified things.
Bill, thank you for the suggestion. Will try that.

Bill, the clock actually came to mind, but I figured I was the only person old enough to remember how those old analog clocks worked, and why they worked that way.
How was like you said, they had a tiny electric motor that would "kick on" to wind the main spring that powered the mechanical movement of the clock. Why was because the clock would not be accurate if simply powered by a DC motor. Varying voltage levels would run the clock motor at varying speeds, and cause the clock to show an hour with 62 minutes or 58 minutes (for example).

There are hour meters still made and used today that have mechanical movements driven by main spring and motor for the same reason, system voltage variations.

But would a 1989 Jeep Wrangler feature an "old school" analog clock?

To isolate the alternator from this scenario, disconnect the wiring from the alternator after first removing the battery negative cable.
Tape the end of the battery wire of the alternator.
Reconnect the battery negative cable and hook up your charger as before.
Wait and watch for the fluctuation to occur.

I was also thinking (later)---
Possibly the computer or clock memory is maintained by a storage capacitor. Instead of the computer/clock drawing a steady load on the battery, it "charges" as needed.

A "leaky" capacitor could be drawing much more frequently.???
I know that's kind of out there, but.....

Mownie and Bill--
Sorry not to get back to you sooner -- haying.
The plot thickens. Still did it with alternator out of the loop. BUT, pulling fuses did give some results. Apparently the wipers have a breaker. Looks like a metal version of a fuse, but larger. With that pulled -- no needle action. Now for maybe more information than you want or need. When the breaker is plugged in with the ignition on, it is warm to touch. Took it out and checked the breaker for continuity and it has continuity. Took another breaker from this jeep's predecessor and put it in -- also became warm when ignition was on. Continuity reading the same as the other one. Needle fluctuates with this one in also.
Now then as if things weren't complicated enough, sometime between the time the needle stuff started and now the wipers have stopped working (yes, with either breaker in) So, I don't know if it's a case of imminent wiper death that caused (& is causing) the needle thing it or whether it's the other way around.
So, Bill and Mownie, if you're not tired of the chase, I'm more than willing to follow your suggestions. (Besides, you're giving my brain a good workout.)

Hoo boy!
It may be that the 7 second interval is tied in with the wiper control switch. Does your Jeep have "intermittent" wiper settings?
If so, one of those settings may have defective contacts that are attempting to cycle the wiper motor.
Wiper motors have an "end switch" which is powered up even when the wiper control switch is turned off.
The end switch is what interrupts the power to the motor when the wiper arms reach the "park position".
Intermittent wiper settings exploit the end switch function to give you that option by feeding the wiper motor a momentary application of 12 volts, just long enough to move the wiper arms off of the end switch park position. The end switch circuit will then carry the wipers through one complete stroke before parking the wipers again. The various choices of intermittent stroke timing reduces the pause time between the short power applications, the end switch does the rest.

You can probe the wires that connect to the wiper motor to see what sort of readings you get at different settings of wiper speed and parked.
As I said above, you should have one wire that remains "hot" even when the wiper switch is off. Intermittent wipers will send the brief power pulse to the motor on the "slow speed continuous" wire. Once you identify which wire works low speed continuous, then check that wire in the intermittent positions to see if this is the "spike" you have been seeing.

Yes, intermittent wipers. Will check as you suggested as soon as we can. Did the warmth of the breaker have any significance or is that typical of a breaker?

By the way, I have been wowed by the breadth and depth of your knowledge and willingness to help anyone over the couple of years I have been a forum member. This isn't meant to be patronizing flattery. You are amazing and a godsend. Thank you from all of us that you have been so patient with as well. I hope to be able thank Bill as well. He is also amazing. (And I'd really love to know how you've acquired so much knowledge about all things mechanical!)

I had good parents who were patient enough to tolerate my insatiable curiosity, especially my dad who encouraged me to learn by setting an example.
He was quite the "self made scholar" and you hardly ever saw him without a book when he was sitting. I followed his lead and became a reader too.
He had plenty of books to "borrow" related to things technical. Looking back now, I smile that he must have bought every book that Audels ever printed.
He had a love for science and technology which I share.
Then, in 1968, I decided I wanted to work in the automotive mechanic trade, so my next move out of high school was to attend Nashville Auto/Diesel College where I took the "full suite" of Auto, Diesel, and Welding.
Above all, I must say I have been fortunate enough to have met and worked with countless people willing to share their own knowledge and experience with me.
I still love what I do for a living, and the science and technology that is an integral part of the craft.

The thing that "looks like a fuse" is probably a resistor.
Getting warm would be "normal" for a resistor.

I've found the cheapest way to gain knowledge is to-----
"pay attention".

Even when you experience things that don't seem to matter that much to you, you can still observe.