I have somewhat similar problem. In my case the furnace will not start unless I completely turn off the main power switch in the trailer. When I turn it back on, the furnace sometimes starts working for a while, until it stops.
My diagnostic is that the trigger voltage coming from the main controller board in the AC to the furnace is very low, about 100mv. I don't know if it is correct.
My short term solution is a jumper wire connecting 12v
to the trigger wire that goes to the sail switch. When I want to get heat and furnace doesn't start, I press the jumper wire 'on' which starts the blower motor, I keep the jumper 'on' until I hear the flame in the furnace comes on. Than I can turn the jumper 'off'. The furnace will keep working on it own for a while, coming on and off a few times as it should, than it stops. The jumper switch is the only way to get it starting again.
So far I replaced the sail switch twice and the controller board in the AC once. I am going to try the controller board in the furnace itself, but I have little hope of it making a difference.
Any ideas will be greatly appreciated.
As a last resort, I am thinking of putting a simple house to thermostat just for the furnace. It will be ugly, but better than waking up freezing in the middle of the night.