how can I get my trailer lights to work properly?

Sounds like you have no earth return wire from trailer lights back to the car chassis, and/or a poor connection in the earth return path from the trailer light bulb to car chassis. When the indicator is trying to work, the only path back to earth on the car is through the filaments of the other lamps.
Check that there is an earth connection from the trailer plug on the car back to the car chassis, it is not enough to rely on the body of the plug and the mounting bolts you must install a wire from the earth pin on the trailer plug to a lug and bolt to the car chassis. Next, check there is an earth connection in the trailer plug, that connects to the earth on the trailer lights.

trover
August 2009