My 1996 Dodge Ram 1500 Tail Lights will work with my turn signals and running lights however, they won't work whenver I engage the brakes!

First check your fuses, then, unplug your brake switch, insert a jumper, if they are now on, problem is with brake switch or adjustment, if you have no power to the brake switch connector socket, keep looking for the fuse.
A Defective Signal Head(turn signals)can cause this as well.

There are 6 wires on the connector going into the switch. What wire is jumpered to what wire to bypass the switch?