I assume you are testing the tow bar electrics by plugging the caravan and checking the lights?
The only common connection to the lighting is the earth wiring. This is the white wire on pin 3 of the 13 pin plug. This is a permanent connection (not switched) and should be easy to check with a multimeter set on a continuity. Testing between the car chassis and the pin should read very low resistance (less than an ohm ideally).
I hope that helps a bit.
Another thought, it’s likely the smart relay is powered up by a switched (ignition) feed. I’ve seen all kinds of contrivances (lash-ups) to obtain this, most often by piggy backing a fuse in the fuse box. Look for an extra fuse on a wire hanging out of the fuse box.