It seems the gas valve is sticking open or the controller board gas valve relay switch is faulty. The clicking is the relay being cycled on and off to no apparent effect. The red flashing light is a soft fault code because the controller continues to sense a flame. It keeps the blower running so the unit does not overheat.
When you increase the thermostat, the furnace is happy again as it needs to keep running. If you turn off master power the relay looses power and drops out.
So, You need a new ignition control board or you can rap on the relays on the ignition board to unstick it and it might work fine for another year or so. You might rap on it anyway and if that works you can have more confidence the relay needs to be replaced. Use the plastic or wood handle of a tool to rap on the relays.
Here is a typical one
https://parts.unitedrv.com/products/...nt=Catch%20All the relays are in the smooth black plastic boxes. There are three in this model. I do not know it this is your particular model. I do know you can get them on eBay for half the price if your model happens to be for sale there. They are less because these are actually universal and are used by many manufacturers so some of the less popular equivalent models get sold on eBay at huge discounts.
Also the controller uses higher voltages for some functions and has a step up transformer on it (to 110V) so careful not to directly touch anything on the board. Wear gloves and only use one hand at a time. Disconnect Shore power cable so there is no continuity to ground. Don't reach in with both hands, this will avoid a serious shock if you accidentally touch something and don't lean against or touch or hold onto the trailer or any metal frame while reaching in. You can wrap on the relays with power off, but it will work best (though not safest) to wrap on it while it is trying to turn off.
Good luck!
Linear Mode
