Agree with most likely cause in your case is intermittent sail switch.. Your furnace is most likely Dometic Atwood AFM series.. If you have outside access to furnace the task is a piece of cake.. Newer Montanas do have outside access panel to furnace..
You CANNOT CLEAN a sail switch... Yes . you can remove any crap that might be around the outside area of the paddle arm but you aren't getting to the root of the issue without taking the sail switch apart.. The case is riveted together.
Spraying contact cleaner, canned air, etc is a feel good repair and the issue will come back quickly again and you wont have heat..
Video i put together showing why its a joke if someone cleans a sail switch.
https://youtu.be/Neg5E0WemgY