Dometic 5 button thermostat

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There is one but the wiring does not go all the way to the AC. The only thermistor connected to the board is the frz sensor.

I have a new CCC2 and two sensors on the way.

I find it hard to believe that there is no sensor for that rear A/C . They are usually located in the Bedroom. Mine looks like a tiny vent ,about the size of half a Walnut!

That is not my case. It is sealed up well. However, there is no remote temp sensor connected to either ac.

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Regarding the short cycling A/C. I was experiencing the same issue with my Atwood unit. Come to find out, the sensor was inside the return side of the AC. There was a baffle that was supposed to separate the discharge and return sides. It had come loose, and the cold air was cycling right back into the return side. I put it back in place and used some duct tape to hold it there. Works good as new.