Electrical Thetford N504 not turning on via car 12v

If you haven't got a manual for it, download here; https://www.caravansplus.com.au/pdf/ThetfordFridgeManual.pdf wiring diagram is handy.

From what I see its a manual operated fridge, looking at your pic of the wiring, from the right the first 2 pins are 12v from van battery, the next 2 are 12v from the tug, there should be power there when your tug is connected, if power is there then look for a fuse on the red/yellow wire, and also check for current at the 12v element, use the element terminal and a good earth, this should show power, if not then either the element or the selector switch, the switches are known to be a weak point............ to get at it usually means pulling the fridge out... Certainly don't go out buying new element until you check the selector switch.

If no power then you will have to back track the wiring, follow the wire colour, take the cover off the van 12 pin check that its not rotten and test that the power is getting through both 12pin connectors, checking using pin earths as well as chassis, if you have an earlier Setek BMS also check if there is a charge to battery when connected to tug as battery charge may be piggy backing off the fridge, if so look underneath van for a flimsy looking shield covering a big birds nest of wiring, could be the spot for a dud connection. ...

The easy way is to just make a jumper lead and go from 12pin to fridge, if it works and the van run doesn't then just do a new run and isolate the old stuff. ............... test power at the element ...

The van battery circuit is just for the fan ................. Do Not Have Mains connected when doing this as 240v is at back of fridge.

Always check terminal earths and chassis earths as earth may be dodgy, many forget about the earth side of things.