Since the furnace is a 12VDC appliance, I doubt the shore power has any effect. You need to access the wires going to the furnace.
Look for a RED and WHITE wire. White is ground, using a test light check for continuity across the power and ground wires. If it has little or no resistance then I would cut the wires and test the LEADS FROM THE TRAILER. If there is continuity, the issue is in the wiring going to the furnace, If not then the furnace needs investigating.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.
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