I know you have thoroughly checked and are checking everything every which way. Just a little more info on the scenario I had going back to the slide umbilical was though it looked like it was plugged in it was infact partially pulled out enough so that the power supply was intermittent and the finally totally not working, this started with the heater then the fridge 12 volt went. Got in there and put that plug In real good, in fact it was working out at an angle hence the progressive failures and the visual appearance that all was good. FWIW I replaced the stock T stat with a digital, programmable one from Home Depot or Lowes, it was 20 bucks or so, a Honywell I think. This ended the short cycling problem that was really irritating.
