I reread the comments on the furnace having to be level left to right in order to work. While I still question this I can see a condition that might cause this problem. Quite unlikely but worth a test.
The sail switch. If there is excessive end play in the fan shaft that may keep the sail switch from making. A way to test this is to have the furnace running and jack the trailer up on the side in question. If the furnace stops as you lift the trailer this could indicate the sail switch is opening.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles