GE Monitor Top Switch/Thermostat Issue?

It was a toss up whether to post this in the repair forum, or in the antique and retro forum, but hopefully it's a pretty basic problem for a pro to advise...

I've got a 1936 GE Monitor Top. It's a beauty and it's been running in my retro kitchen for over 3 years. All I've done is clean it up, paint it, and replace the door seal. It still runs great. Except...more and more often it's deciding not to run. That is, not to switch on.

From time to time I'll notice it's not cold when I open the door. It was running, but then for some reason it stopped cycling. All I have to do to jump start it is to turn the switch to "off" and back to "on" again, and it starts right up. It gets cold again just fine and displays no sign of trouble. Maybe for a day, maybe several days. But it's getting to be more of a daily occurrence.

I've been through the housing for the contacts, and I've cleaned the contacts and everything else there. Those are fine, or I'd think it wouldn't run at all. It seems to me whatever is sticking is in the switch, or maybe the thermostat. I'm a little bit lost there, though. I can see what's going on with the contacts and the basic wiring. Can anyone help me troubleshoot from there?

Thanks much.
Bill