It was one of those weekends. Being rather cold out, the air conditioner (of course) decided it was going to start running. When the usual check of my Nest thermostat didn’t provide any insight, I ...
If you swapped the suspect 2-wire non-programmable with the known good 2-wire programmable from the bathroom and it works properly, there is no other conclusion. The 2-wire non-programmable is broken.