I doubt the original wiring is up to the task of running a fridge as it will be pulling in the order of 10-15 amps and the voltage loss to the rear of the car and caravan will be substantial.
You should really be running separate heavy duty cable from the man or aux battery and using an Anderson Plug at the rear of the car and a separate cable in the van to power the van when being towed.
Garry
				
			 
			
		 
			
				
			
			
				REMLR 243
2007 Range Rover Sport TDV6
1977 FC 101 
1976 Jaguar XJ12C
1973 Haflinger AP700
1971 Jaguar V12 E-Type Series 3 Roadster
1957 Series 1 88"
1957 Series 1 88" Station Wagon
			
			
		 
	
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