Can you tell us the model of the A/C and the thermostat?
The 12 volts for the thermostat comes from the battery/converter (Power Panel) through the A/C control box. There should be a fuse somewhere that supplies 12 volts to the A/C (& thermostat).
Keep in mind that Dometic analog thermostats switch the negative side to control the functions, and not the positive side like most other mfg's do.
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Salem 29RKSS Pushing a GMC Sierra 2500HD!
Gotta go campin!