I put an electronic thermostat in my unit. It took some mental contortions to figure out the wiring, and the addition of a small switch from Radio Shack to control the fan.
My unit was performing somewhat the same as yours. Start, run, stop, then immediately restart. I tried to find another RV thermostat, and discovered they are made of gold.
Now, I can program the beast to cool down or heat up at certain times of the day. It is very nice to have the heater come on in the cool mornings, just before you get up.
Just a thought.
07 TM 40D;ISL 450 Cummins(upgraded). Very happy w/coach
Gnarly toad to scoot around.
Geocaching, hiking, fishing, National Parks, Civil War sites.