A point to keep in mind on the heat and air is that the thermostat uses 12VDC as only acts as a switch to turn the 110AC on/off.
When there are no lights, etc. at the thermostat, I tend to think of 12VDC problems!
The issue is a design thing where the big air unit needs lots of power and we get it from 110AC. But those heavy wires are not nice to fit a half dozen or so into the little box on the wall. So they use little wires and power at the thermostat to control a big relay up on the AC unit where they start and stop the big wire 110AC!
If we know what year, make and floorplan you might have, there are often online drawings where we can sort out which breaker or fuse might be involved!
Maybe do a quick test to see if the furnace will start the blower when the thermostat calls for heat. Just as a generic idea, the 12Volts from the furnace may run the thermostat for both heat and cool. If the furnace blower doesn't come on right away after setting for heat, maybe a check in the "load center" where a bunch of 12Volt fuses are located may turn up one labeled for furnace?
Click this snip for better view!
Tell us which RV if we need to chase it further?

Consider this a first shot random guess!
