Don't know how to ground the lights, since they are mounted on the galley door, and that door is just plywood and aluminum.
For a tail light/brake/turn signal light fixture, there are two wires coming out of the fixture.
Both are positive.
One posititive supplies the tail light function.
The other positive supplies the brake light and turn signal function (brake and turn signal both work on the same single wire).
If there is a third wire, it is a negative, or ground wire, not many lamps have them.
Most often the lamp is attached to a metal surface that is tied to the metal chassis, but if it is not, you can run an extra wire to each lamp, and use the screw or bolt the lamp attaches to the body with as the connection point, or, run a jumper wire between the steel chassis, and the "floating" metal panel.
A wire from the chassis to the lamp is best.
If you have multiple lamps, one ground wire can be run, connecting all the lamps.
It is easy using an electric tester or meter to determine which wire supplies which function.
Turn on the tow car ignition, and choose a function, say right turn signal.
Place the ground lead of the tester on a good ground point, then test each wire until the test light blinks, or the meter display flashes between zero and 12.5 volts.
Mark the wire with its function, and then do left signal, then tail lights.
Often, even when the ground connections on the trailer are wired correctly,the ground is lost between the tow car and trailer (the tow ball is not meant to be the ground connection).
Be sure you have a dedicated wire that connects the tow car chassis, to the trailer chassis.
Better yet, is to have a wire that runs from the tow car battery, through the wire harness to the trailer chassis, and lamp body.
Rob
Waiting for "someday" will leave you on your deathbed wondering why you didn't just rearrange your priorities and enjoy the time you had, instead of waiting for a "better" time to come along...