It should be a fuse - I had exactly the same problem when I bought a caravan years ago. turned out that the trailer socket was wired to the rear lights through a fuse that was too small for the extra lights. Check that the parking lights come on - it is just possible that it is the contacts in the switch. Otherwise it has to be a coincidental wiring problem, or more likely, a coincidence of bulbs burnt out (how long since you checked the tail lights?). 
Possibly an earth problem - do the stoplights change in brightness when the tail lights are turned on - check with a lens off whether both filaments light up with the stop light? (assuming the extra drain from the trailer caused the common earth for the rear lights to go open circuit). Also check if the number plate light is working - if it is the problem will be somewhere in the actual light units, I think. 
John
				
			 
			
		 
			
				
			
			
				John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
			
			
		 
	
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