My money is a bad switch or fan. Loose connections would likely be switching on and off intermittently, but it cant be ruled out. You can either replace the switch since they’re fairly inexpensive, or test the load voltage with the switch on as kudzu was eluding to.

The most likely cause is gunked up or worn out fan motor bearings.

The most common older bath fans (and some newer ones) have a standard AC receptacle inside that the motor plugs into. You usually have to remove the grill and the motor frame to get to it. Do so, and try plugging a light into the receptacle. If the light works, replace the fan.

Or, if you're cheap, try a little WD40 or 3-in-1 oil on the fan bearings, This is usually a temporary fix. They'll gum up again in a few months or (if you're lucky) years.

If the bearings are bad, wouldn't the fan motor still hum or make a discernible noise to hear?

It might hum, or not. It's a pretty small motor.

I had a bathroom fan like this in one of my rental houses. It didn't hum, at least not that I could hear. It just took anywhere from several seconds to a few minutes to finally get going.

I don't recall the similarly afflicted range hood fan humming either, but it's been longer on that, so I might not be remembering it correctly.

Many times a gunked-up motor will restart just fine, once it's warmed up and the glop has softened some.

FWIW, an old-timer I knew about 50 years ago told me about fixing plug-in electric clocks (anybody else remember those?) that had quit. He'd take the works out of the cases and soak them in a coffee can full of kerosene! I report this for entertainment purposes only -- I don't actually recommend doing it. :(

Old timers are the best, they could fix damn near anything, and while using a method they came up with on their own.

> Old timers are the best...

Yep! And when the TV or radio conked out, you pulled the tubes, took them down to the hardware store or even the drugstore (really), and popped each tube into their tester. You bought a replacement for the one that read in the red "bad" or yellow "weak" zone, and you were back in business.

Today if your computer quits, you're lucky if replacing the entire motherboard fixes it.

OTOH, when you adjust for inflation, some of the more expensive TV tubes back then cost as much as a cheap motherboard does today.

To get this back on topic, with all the stuff that's disposable today, I was kind of heartened to see that you can still buy replacement motors for Broan and Nutone bath fans.

Its because theres so many of those damn cheap fans. I’ve replaced one of those fans & motors myself, replaced two others with Panasonics, and still have one more in the house. They liked them alot here.