OK, I see you have done your home work. Good!
You will need to begin by checking the Purple wire circuit leading out of the key switch from Terminal "A".
You can't simply check for "continuity to ground" using an Ohmmeter for this because there are a number of devices fed by the Purple wire and they are all directly connected to the Purple wire circuit. This means that even a perfectly good wiring harness and all devices will show "continuity to ground" when an Ohmmeter is connected between the Purple wire and the chassis ground.
You will need to physically examine the wiring harnesses/pigtail leads that serve each of the devices to see if some part of the machine has chafed, pinched, or burnt through a wire.
Here is a list of the devices that feed directly from the Purple wire circuit:
Hour meter
Auxiliary power outlet (12VDC accessory power socket)
Seat relay
Seat switch
PTO switch
Voltage regulator
Oil pressure light (only the circuit LEADING TO the light bulb, if the wire to the OP switch shorts it simply turns the OP light on......not blow a fuse).
If you DO NOT discover a damaged wire serving a device, you will need to move to the next level of testing.
The next level will require that you unplug or disconnect all of the devices in the above list.
Next, get you a supply of 20 amp fuses (yes...20 amp) to replace the OEM 30 amp fuse.
With the key switch connector in its proper place on the switch and the battery connected..........turn the key switch to the RUN position. If the 20 amp fuse pops, you might as well begin removing body panels so you can inspect the main wiring harness loom for damage that is concealed from easy view.
If, however, the 20 amp fuse does not pop.....begin re-connecting the devices "one at a time" (turn off the key before you re-connect a device). Check the fuse each time you re-connect a device and turn on the key. Be sure you are sitting in the seat as though you were doing a normal operation.
When you re-connect a device that pops the 20 amp fuse, you have identified the circuit that is shorted. If it turns out to be a relay that pops the fuse, you can swap relays to see if it is the relay itself, or if there is a problem in the wiring leading OUT of the relay.
If swapping a relay DOES NOT cure the fuse popping, there is trouble beyond that relay.
If this does not steer you to a resolution, post back and we will try to go deeper.

Thanks for the help.

I disconnected the devices on the purple wire circuit. I found that I could re-connect all the devices except the connector leading into the engine (regulator). When this was disconnected, I could place the key in the run position without blowing the fuse and The starter would turn when the key was in start position.

Unfortuneatly I did not have time to trace the wires any further. They all go under the engine shroud which appears to be held on by a zillion bolts and screws, most of which are nearly impossible to reach. LOL Any guess what I may find in there?

thanks again

Being as it is a Kohler, one or more of the magnets INSIDE the flywheel may have come "unglued" and piled up on the alternator stator coils, resulting in some serious damage.
The picture below is from an old thread posted by a member who had a similar issue with his Kohler.
The red Xs indicate loose flywheel magnets that have stuck to the steel laminates of the stator coils.
Bent (and shorted) coils are indicated by green lines.

{{gwi:327887}}