Fridge behaving strange

[Bradely]

Hello, I am new here, own an Ocean T6 registered 2020, fabulous car so far, but I experience some strange fridge behaviour:
- It does not work for more than a couple of minutes off grid (so without engine running or connected to external 230V), and only after repeatedly pressing the fridge button
- It works when the engine is running (though I may have to press the fridge button up to 10 times before it works)
- It works when hooked up to external mains power 230V
I just installed 2 new leisure batteries hoping this would solve the issue but it didn't. Voltage on the display is 12.7V, so far away from the low voltage level threshold.

Another strange thing: last weekend we slept in it for the first time, it was connected to the mains. I set the fridge at level 1 but it kept running the whole night and in the morning a water bottle and the strawberries were completely frozen. So looks like something is wrong with the temperature control as well.

Any ideas what I should do? I'm pretty good at DIY, read posts on faulty Danfoss controllers on the T5, is the same controller on the T6? Can it be reached at all?

You are correct the C and T are connected together but with a resistor in the circuit.