Darwin, I like the pencil eraser idea, but remember the ground contact is the sides of the socket, that's where the brush comes in. That KD brush also has bristles on the end to clean the contacts. Barry; now you've thrown a curve in here, in that the brake
lights work. If you have a single bulb
light, the turn light & brake light are the same filament in the bulb. Is this problem also in your tow vehicle lights, make sure front & rear work, you could have a turn switch problem. But hope for the easy fix, clean the socket & replace the bulb. I had an odd situation a while back, blown fuse for turn lights and dash gauges, problem was a short in the trailer tail light bulb. I've never seen this happen before, and when I was a truck mechanic we were fixing lights almost daily. Bob