Winchman:
When you run the wire from the battery to the trailer frame, and it makes everything work correctly, that will prove that it is a ground problem, but it won't yet tell you whether the fault is in the truck, the connector, or the trailer. To do that, you have to peel back the insulation on the truck wire (from the plug to the truck frame), and run the test wire to the bare spot. If that fixes it, then the problem is in the truck. If it doesn't, the fault is in the trailer or connector.
These days, even before I run a wire from the battery to the trailer frame, my routine on any trailer electrical problem is to remove the truck and trailer ground wires from the frames, clean everything, with a wire brush and/or sandpaper, and reassemble. I've started coating them with dielectric grease, but only have 6 months or so doing that, so I don't know if it helps.
On my truck, a 1989 Chev, the wire from the trailer plug goes to a bolt on the outside of the left rear frame rail underneath the bed. That has gone bad three times in 13 years, but cleaning has fixed it each time. There should be a similar connection on the trailer, where the ground wire from the plug, (usually white, but sometimes whatever color the guy wiring it had close to hand) goes to a bolt on the frame. On either the truck or the trailer, you can't tell by looking at the connection whether it is good, unless the wire is broken off. Even putting a meter across the connection won't tell you anything for sure, since the connection may be bad only when you try to get it to carry more current than an ohmmeter puts out. With a normal modicum of luck, however, cleaning the ground connections will fix the problem and further diagnosis will be unnecessary.
Good luck
