[Out of ideas?]

Does your guage dash lights work okay? It's definitely and open circuit between your headlight switch and the taillight bulbs. Try checking under the bed of your pickup, if it has ever been in an accident and any removal of the taillight housings, they may not have been replaced correctly or the ground wire from the taillight housings may have become disconnected. Also, check to see with an ohm meter to see if there is any current at all at the taillight sockets with the parking lights turned on. Hope this helps?