Looking for a ground wire

mr_andyj wrote:
Ground is ground. 2 amps is not a concern, but higher amperage might burn out the little tiny thermostat wire, not a concern here. Ground is ground, so if ground is issue with your pwm then any ground will be an issue. The steel camper frame is ground also, the entire frame of the camper is ground, all the ground wires are ground, they are all connected to the frame and to the negative post on the battery, ground is common to everything.
The only concern, as stated, is how much amperage will be flowing through your chosen ground wire.
I dont think there would be concern with your thermo wire, but try it, if it works then it works, job done.

Ground WIRE is not always "ground".

That would be a blatant disregard of proper electrical wiring and a violation on NEC rules.

120V ground wires must terminate in the 120V breaker box on the ground buss. Yes, the ground buss must be bonded to to trailer frame but the 120V wiring has the potential for 120V currents which can cause voltage potentials on any of the ground wires that can cause issues like GFCIs false tripping or even higher voltage potential than 12V on your 12V system..

120V systems ground WIRE and 12V systems ground WIRE should never be exchanged or substituted or mixed.

I would also not recommend using the furnace T stat wires for 12V ground as the "ground" you find there goes through the furnace control board and will no longer be at ground potential when the T stat calls for heat.

Since there is no real 12V ground available OP will need to get creative on pulling an extra wire for the ground. If the location is close to wall trim you might be able to remove the trim carefully and carve out or drill a hole to thread the wire through the wall stud. Check at floor level to see if you can fish a wire from the floor up. Often you can drill holes just large enough to thread the wire but not too big to cause major damage that can't be hidden with some trim.