DC Power from Fused source is AT furnace all the time...same DC source goes to one side of thermostat
When Thermostat Closes DC goes back to circuit board to trigger DC power to FAN
What is interesting is that you say BOTH will not start
Are they controlled from Same thermostat?
What 'power & grounds' did you check?
Checked using voltmeter?
What Year/Model is RV?
Does the DC for furnaces go to A/C Unit control module then to T-stat?
Here is the wiring for the Furnace ...but RV wiring is an unknown
Could be the On/Off CB switch (On furnace) could be tripped
Could be bad wiring connection at circuit board
Could be bad circuit board