Ground faults can give some really screwy readings. If that picture is an actual picture of your truck, the level of rust on the frame rail may be a partial indication of the problem.
Many electrical components may be "grounded" to whatever metal "frame" or "body" piece is handy. As a combination of factors build up over time (corrosion, friction wear, etc) the various components of the vehicle (Cab, frame, bed) may become electrically insulated from each other. As resistance to ground builds up these odd things may occur.
It's very possible that the ground at that point in the wiring harness doesn't go all the way back to the negative terminal on the battery. It may be attached somewhere nearby to the frame or body (bed). If that ground circuit has any corrosion at all in it, it may have a resistance value greater than zero (dead short).
Let's say the lights are on (brake lights, running lights, whatever) and they are grounded to the truck bed. The truck bed is bolted to the frame and the frame is bolted to the cab and the battery is bolted (grounded) to the cab & engine. Any creeping corrosion at any of those connection points can increase the resistance at each point.
The metal mass of the bed and or frame could likely provide enough of a ground mass to light the lights even if the circuit back to the negative terminal of the battery was "less than perfect". Maybe the lights wouldn't be as bright as when the truck was new, or maybe the flashers wouldn't flash as fast, but it may be hard to detect.
The way you would see it is by taking a reading from "ground" on the + voltage side of whatever defect was in the circuit to a "better ground" on the other side of the defect. A voltmeter is designed to avoid putting any loads on the circuit being tested, so what you could see is a positive voltage reading on a "ground point" that has a rusty connection between it and the negative terminal of the battery.
Finding the bad connection is the tricky part.
If you are reading +12 vdc on the ground pin of the 4 pin connector, then whatever that pin is grounded to has some resistance between it and the negative terminal of the battery. I will *assume* you are finding ground (with your voltmeter) somewhere close by, probably the frame (trailer hitch bolt etc). The wiring harness is probably grounded (along with tail lights and other accessories) to the truck bed/body. That's a place to start.
Take a stout piece of heavy wire and make yourself a new ground strap between the bed and the frame. Both connection points will have to be cleaned down to bare metal (you can touch up with Rustoleum later). See if that fixes it, if not, make another ground strap for each connection back to the battery negative post.
Eventually you will find the fault.
NOTE: If the voltage is negative (-12 vdc) on the white wire in the harness, it's another problem.
