Older thermostat acting up

[Enduroma]

can someone help me understand how my furnace is wired in simple terms?
I have a 2000 class C motorhome with a propane furnace and a dometic thermostat. there’s also an old air conditioner on the roof. Pretty standard set up as far as I can tell, and everything is in pretty decent shape.
The problem though, is that I get a clicking sound from a module in the AC unit on the ceiling, when the FURNACE reaches a cut out temperature and tries to turn off. Cycles on and off.

so I’m trying to determine if I have a thermostat problem, or a problem with the module in the AC unit on the ceiling? Any insight here is appreciated!

I took apart the metal control box in the AC unit, blew out the dust, and secured all connections. 3 amp fuse there is fine.

Some other data:
Class C is 24 years old
Furnace: Hydroflame 8531
Thermostat: Duo-Therm by Dometic
Battery is charged (clicking also happens on shore power)
Control box in ceiling: Duo-Therm E155095
Lots of propane in tank

Thank you in advance!

[Skip426]

Is your t'stat a four button unit ?

There is a pdf in the " Files " drop box ; heating and cooling section called ; DuoTherm CCC , that may provide help .

[Enduroma]

No, it has a sliding elector for the temperature and three switches for mode, fan and hi/lo.

I’ll take a look through that file as soon as I can.

[Enduroma]

Photo

[Enduroma]

[Enduroma]

That file is informative, thank you. This is my system albeit with a different thermostat controller. See photo above. File doesn’t help me explain the clicking in the AC unit when furnace attempts to shut off.
I’m tempted to just start replacing components one by one but I’d love a little more wisdom before buying things I don’t need.
Thank you.