This is what you posted.
"The thermostat itself doesn't even look like the manual version. It's just a simple white rounded box. The top half has temp markings and a plastic stem that I pull up or push down (right or left) and the bottom half is the same except there is no stem - it reflects the actual temperature."
That does NOT describe a RVP(Coleman) or any RV Tstat. It appears someone has changed out the original with a Home type tstat. If so, they probably miswired that tstat, which is a common problem when novices attempt to wire a home tstat to a RV. Are you the original owner of the RV? The Roof AC is indeed 120 volt breaker controlled. The FURNACE is 12 volt dc controlled. The Furnace 12 volt fuse will be located in the 12 volt fuse panel for the RV. If the fuse is NOT labeled, then have the furnace run and pull each fuse until it stops. Now, the bad news is this, Some RV's use the furnace 12 volt power to power the wall tstat and the controls for the roof AC unit. The roof AC unit, the controls are 12 volt powered. The 120 volt to the roof AC is just for the Fan motor and the compressor. Doug
I should have mentioned. IF the wall tstat is a RVP(Coleman) it will state this on the tstat. Doug