I had a similar problem on my Chieftain. The furnace blower would come on all by it self with the thermostat off. After a lot of testing I found a bad ballast sending a RF back down the light switch wire that was near the thermostat wire. I tested it out by disconnecting the suspected fluorescent light. My problem ended when the light was disconnected. I switched the light with one toward the front. No more problems. When I was researching my problem I found situations where TVs would go on & off all by them selves when a bad fluorescent light was on.
Good luck and please let us know how you fix your problem.
Don & Bev Morgan Weyauwega WI, 05 Itasca Horizon 40KD, 400 HP Cummins, Adopted by a great couple, Toad 07 Saturn Vue AWD, Air Force One, TST 510 TPMS, Mayor of Weyauwega 2007 - 2013, Waupaca Co Board Supervisor 2010 - 2014