When operating the solenoid manually (direct connection to a battery), it works every time. However, when attached to the system, it doesn't.
I'm the 2nd owner. The furnace is likely original to the trailer. I see no evidence to the contrary. That makes it 10 years old. The overall condition of the furnace is in good shape. No rust spots, corrosion, pitting, etc. I found a couple wires where the mice nibbled at them, and fixed that.
So, it comes down to the solenoid, which works when operated manually, doesn't work when connected to the circuit board.