I agree with XC70Bob about a bad earth, I would look at a loose connection on pin 3 which is the earth return for all the road lights. I would start at the plug/socket then check the other end of the wire, i.e. earth connection in the car and the earths within the caravan.
A quick check is to turn lights on and hazzard warning on that the same time and see if the other light dim and brighten as the hazzards flash.
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