How, precisely did you do that? Your problem smells totally like a floating (high resistance) ground. Troubleshooting that is relatively simple if you use one trick - take your jumper cables, and ground the trailer frame to an unpainted part of the TB frame. If you used an ohmmeter to check out the connector ground, those aren't too accurate below an Ohm, and you really want that ground to be below 0.1 Ohm or better. If you used the meter in voltage mode, even a high resistance ground would read zero volts.I have checked the receptacle ground on the car...
Another trick if you have a good meter and can get the lead onto the ground wire in the connector is to measure it while the truck's lights are on and you have the problem. See if it's near zero volts or bounces around to 6-10V.