One way to test the furnace starting is to apply 12V to the "W" lead at the thermostat after disconnecting it from the thermostat. proving whether the thermostat or furnace is the troublemaker. You will likely have to take the cover off or dismount the thermostat to gain access to these leads. Both 12V (which powers the thermostat) and the "W" lead are available there. This should start the furnace blower.
If it does not, I would try and find a fuse for the furnaces 12V supply itself. (I'm voting for this as the issue!!) You could check at the furnace using a voltmeter for the presence or absence of 12V. (The coach/trailer wiring is all connected to the furnace, likely with wire nuts, next to the furnace, a convenient spot to open/test). As mentioned previously, nothing will happen unless the fan is running at full speed. When you get that working, after a short delay, you should hear the furnace try to ignite (clicking sound -"sparking"), When it does, the clicking should be replaced by a low "roar". Note: With an electronic thermostat, after setting the temperature, there is usually a short delay before anything (heat or air) kicks in. Listen for a small click from the thermostat relays.
I hope yours has a better access than my SF42. I had to remove the stove and open a wooden box underneath it, no access from outside!!!!