I've never actually thought to check whether my fridge actually does anything when connected to the car, i just assume it auto switches to 12V.
On the other hand, i always chuck a couple of freezer packs in there before we leave to help keeps things cold.
I'm not sure why people are so worried about caravan fridge operation whilst towing.
Surely whoever fitted the towing electrics will know perfectly well what is required and fit accordingly. It amazes me to think that some feel a professional tow-bar fitter doesn't know his/her job! I would expect a few disgruntled customers making their views known if the fridge did not perform adequately.
I would also imagine that everyone turns their fridge on (if possible of course) at least 12 hours prior to beginning a journey. If they don't then I respectfully suggest they should.
We've never had a problem with any fridge and that includes overnight ferry travel as well as towing in the upper 30ies in Europe.
I imagine that older fridges/caravans will not all have the sophisticated electronics of the newer ones. In our case I always turn off the gas when towing and set the fridge to automatic. Whilst the fridge will prefer electricity over gas if available turning the gas supply off is good practice anyway for obvious reasons whilst towing. As soon as the electrical supply is turned off the fridge beeps and as soon as the car engine is started it stops beeping and works on 12v. The fridge is invariably cold upon arrival at a site!
Am I the only person who has never questioned the operation of my fridge whilst towing?
As for stop/start technology then as previously mentioned whilst towing this should be turned off if the car does not automatically turn it off. The reason, I believe, is to allow the turbo and cooling fans and any other cooling oil circulation to continue when stopped since towing will have placed a greater stress on the engine and probably increased temperatures.