Typically the +12VDC voltage is applied directly to the thermostat (RH and RC pins – thermostat switched on to heat position) and a call for heat closes a relay in the thermostat which then supplies the +12 VDC to the Atwood furnace control board/sail switch etc. Since you said all the wiring in the furnace (outside access) looks solid, clean, dry and new..... possibly the time you opened the outside panel and the furnace came on was only coincidental with the thermostat calling for heat? You said when not working, there is no power on the thermostat. I assume you are measuring DC volts on the RH terminal of the thermostat? Do you hear the thermostat relay clicking when it calls for heat? Does the thermostat use its own batteries for internal control of its relays and if so are the batteries good? Perhaps a bad 12VDC connection at the thermostat RH and RC connections; or where +12VDC wire in the wall connects to the thermostat RH/RC wiring?
I think your manual can be found here: (Schematic on page 8).
https://manuals.heartlandowners.org/...wood%20AFM.PDF
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