Rear lights. (Blinker, running, reverse, brake)

If I understand right, when you turn the headlights off, the rear lights work properly. If that is correct, suspect a broken ground wire for the rear lights. There is going to be a clue in that the rear lights aren't really working properly even though it may look like it. In this case, if you turn on only the left signals, you will likely find the rear one stops working if you remove the right bulb. That's because with a broken ground wire, current for that bulb can't get to ground, but it finds an alternate path through the interconnected tail lamp filament, then over to the right tail lamp, then to ground through the front running lights. You may find the front signal lamps lit up very dimly at the same time.

You can also turn on the tail lights, then test for voltage on the brass base of one of the bulbs. You should find 0 volts there, but if there's a bad ground, you'll find between 4 and 8 volts.

Fixing what? You have to tell me the results of any tests you did or any other observations. If what I suggested previously proved there is a bad ground, start by following the wires to see if you come across a break in one of them. Since it sounds like all the lights on both sides of the rear are affected, the break won't be near either tail light assembly. It will be where the wires are spliced together from both sides. One of the more common causes is when someone used Scotch-Lok connectors to splice in a trailer wiring harness. Those connectors don't seal out moisture, and the vehicle's wire will corrode in that area.

When you do find a break, look at the condition of the wires. If they are a dull brown or a dark brown, they are corroded and solder won't adhere to them. You'll have to cut the wire and insulation back until you run into nice shiny copper to solder to. That can be as much as two or three feet wire if the insulation has been cut for a long time. Splice in as much new wire as necessary.

For a cheap, temporary fix, if you did find voltage on the brass sockets, you can solder a new ground wire to one of them, then bolt the other end to the truck body or frame. That's not a professional repair but it will get the job done. Most likely you would only have to do that to one side, but if the original break is at the splice for both sides, you may need to run a new ground wire for each side.