The air conditioner fan on (and fan speed) switch doesn't need power to operate. The rest of the thermostat functions probably do. I would check the 12V supply and ground at the thermostat (which would be two of the wires from the air conditioner).
I checked the breakers, they seem fine. The heater does not work, & the fan in the overhead AC unit will work when the Tstat is set to fan, but when the switch is moved to AC it shuts down. I'm totally confused....
Go over everything from power outlet, breakers, and plug ins (is it plugged or hard wired?) Then gently pull the t-stat and verify wires.
4 whopping cylinders on Toyota RV's. Talk about great getting good MPG. Also I have a very light foot on the pedal. I followed some MPG advice on Livingpress.com and I now get 22 MPG! Not bad for a home on wheels.