Running parking lights on my trailer won't work?

Look at the rear lights on your truck. Are the brake lights and the turn signals separate bulbs? If they are, you need an adapter harness on the truck to run trailer lights that use the same bulb for the brake and turn signal.

The good news is the parking lights are on their own circuit just like they've always been and troubleshooting should be very straight-forward. First of all, if you're testing for voltage at the plug with it disconnected from the trailer, that CAN give a false reading with a digital voltmeter. Use a test light instead. I can explain why if necessary. Try to back-probe at the connector with it still plugged in. Since the trailer lights work on another truck, half the possible causes are already eliminated. If you find voltage at the plug, suspect a bad ground wire for just the trailer harness on the truck. You should also find the brake and turn signals do something unusual. They can find an alternate ground through other lights on the truck, in which case they might appear to light up but they won't be as bright as they should be.

Your last sentence is correct. Just to back-track, you tested on your truck with a test light but was the harness plugged into the trailer when you did that?

So if I have this right, you have the connector unplugged from the trailer and the test light lights up when you turn on the running lights but the trailer's running lights do not light up when you plug it in.

I'm sure you already checked the terminals in both connectors to be sure one isn't partially corroded away. That leaves excessive resistance in the circuit in the truck.

I think I would try connecting a single bulb right at the truck's connector to see how bright it gets. Test lights draw very little current so that won't have a hard time lighting up. Each tail light bulb draws about 3/4 amp. That WILL have a hard time getting through if there's some resistance in the circuit. A good place to look for excessive resistance is if someone used "Scotch-Lok" connectors to splice the trailer wires to the truck's harness. Those do not seal out moisture and will always corrode. If that bulb lights up, add a second bulb. If the first one dims noticeably when the second one is connected, that too points to excessive resistance.

I can think of one other possibility. I don't know how your harness is wired to the truck but I would expect GM planned on people pulling trailers, however, there is a part called a "positive temperature coefficient, (PTC), that is a semiconductor device that replaces a fuse. When the trip current is reached, it goes open circuit to protect the wiring, then when the short is gone it resets and lets full current flow again. It is not the same as a thermal auto-resetting circuit breaker. Chrysler started using them in the '96 Caravans. I don't know if they were ever used in any other brands but it's worth mentioning. Those parts are designed for a very specific current and adding trailer lights could exceed that rating. If by some chance your truck has those, connecting light bulbs at the connector as I just suggested will suddenly make the entire circuit go dead. For that circuit there will be a different wire provided specifically for the trailer harness.