Best way is to have a multi meter, with plug wiring diagram test each terminal to see that they match, do same for van, now to do it on the van, plug it into car but remove cover on van socket and test terminals, noting colour of wire matches the plug terminal number, with meter, test 12v wires at back of fridge (remove lower vent) (black is postive, white is negative on Jayco wiring but fridge wires will be red pos and black neg )
and for power to van well thats easy, with van still plugged into car turn battery in van off and then turn a light on, if light doesn't come on then something is wrong.
The power to van wire goes to a birds nest of wires under van and split feeds to fridge and Setek which in turn will charge your battery (so long as battery is turned on) the Setek will not power the fridge as the fridge is isolated from the van 12v supply, running it from a battery which isn't getting a constant high flow charge will flatten the battery in 30 mins thats why you must always disconnect when you stop the engine unless you have a isolation device fitted to your 12v supply from car.
So simply to check if you 12v supply to van is working, turn battery off and a light on, light works all is good.