I'd check the plugs, sockets and cable for damage, dirt, corrosion etc and give them a good spray with WD40, otherwise check the individual cables haven't been miswired or poorly connected by a previous owner, possibly?
Was it previously working ok & fault has just developed? If so suspect poor earth probably due to corroded wiring in any of the plugs/sockets connecting caravan to car.
If any of the plugs/sockets have been recently rewired it's possible wiring has been incorrectly connected inside plus or sockets.