What could be wrong when there are no brake lights or turn signals in the back but you have running lights and all the front lights work on a 1981 ford f150?

Have you checked to see if your back lights are not burned out? That could be the problem.

If your bulbs are good then you have a broken set of wires going to the rear lights, (look by where the trailer wiring was installed if so equipped as that's a common area of problem for broken wires. Hope that helps. i had the same problem with my 1985 south wind it had a exposed wire that ran right behind the brake peddle throw the floor Bord they did make the hole big enough so when the pushed the wire throw it striped it so every time i hit the brakes the fuse would blow. and i would have no lights. don't know if this helps you, good luck .