On the furnace, most are wired like this...
The thermostat that can control the furnace, the signal goes from the thermostat, the a controller up top in the air conditioner. Then a pair of wires from the heater control circuit on that board comes down to the furnace and interfaces with a pair of furnace wires (blue and a blue with white stripe).
That circuit tells the furnace to turn on / turn off. The board in the furnace has the logic to control the combustion, fan etc. of the furnace.
You can disconnect the control wiring from the blue / blue-white (on a Suburban furnace), then short the blue / blue-white to test. The furnace should come on with those two wires shorted. In a previous RV, when my AC that controlled the furnace "had a bit of a melt-down", I installed a separate (2 AA battery powered) thermostat just for the furnace. Worked great.
See this picture for the OEM wiring "at the furnace" (on a Big Country - could be the same on your TR). Note the wire colors on the zip-cord of the coach wiring that interfaces with the blue / blue-white wires of the furnace. I hope this helps.