2005 F250 Trailer lights

Not sure if you know that much about electrical wiring so I will go through it like you don't.
Take the trailer plug out of the female socket at the rear of the car, turn your running lights on, go to the female plug and using a test light check to see which one lights up the test light, that wire will be the running lights wire.
turn the running lights off and turn either your left or right indicator on and check at the plug to see which wire lights the tester, do this for the opposite indicator as well.
Turn the indicator off and get someone to hold their foot on the brake while you test the plug for power.
check the male plug at the rear wire terminals by putting it in the female plug and perform the same test as the female plug, if you have power to all the wires at the rear of the male plug go to the lights at the rear of the trailer and perform the same tests as before.
to get the both rear brake lights to come on you have to run a red wire from the brake light on the live wire side to the light on the opposite side to give it power when you apply the brakes for it to light up.
Turn the ignition on and turn your left or right indicator on again and check the wire for that side, if that is ok do the same for the other side then the running lights, you will have to run another wire off the running light wire to the opposite side of the trailer to give that side power to the lights
ther should be an earth wire from the plug that has to earth the trailer, all the lights also have to be earthed as they will not work if they aren't.
Try that and see how you go, if you do it right they should work for you