On a hunch, I suspected a poor earth was causing the trouble. The jump leads were pulled from the locker and clamped onto the Dodge tow hitch and the trailer towing eye, creating a new earth connection. The lights were turned on again and instantly, nice bright lights!
The wires in the trailer plug and socket were connected as they should be, so I cleaned all the earth terminals on the trailer, but it gave no improvement. On the Dodge, the earth wire from the socket disappeared into the Dodge wiring harness and I've no idea where it went from there or where it was connected to the chassis.
Rather than waste hours trying to chase where it went to, I made a temporary jumper wire from the white trailer socket wire to the Dodge chassis to make a new earth. The lights then worked as they should. This is the tail light and indicator.
With the problem sorted, I made a permanent connection from the Dodge chassis to the trailer socket earth wire and checked everything once more. The last picture is the tail and brake lights. All the lights were working properly so everything was packed away in the garage again.
