Okay, this is a good start. If you have not already done so, download a copy of the FSM from this site. (If you are on a computer, the link is in my signature.) Also, look at Blue's tech tips for a copy of the full wiring diagram. I think there is even a color copy of the wiring diagram floating around this site somewhere.
On page BE-14 of the FSM, you'll find the reverse light circuit. The diagram shows that one side of the switch gets power from the fuse box, and the other goes to the taillights. Neither side should be grounded. Since you say one side of the switch is grounded, let's assume that is the side with the bulb sockets. Unplug both of your taillights at the taillight panel. Check the wire that had continuity with ground to see if it is still grounded. If it is not, the problem is at a taillight. That might also correspond to the dying problem happening with the turn signal.
If the wire is still grounded after that test, break the connection at connector C-4. Test again. If it is grounded, the problem exists between the switch and connector C-4. If it is not grounded, there is a chance the body wiring harness is damaged, probably by a screw and is grounding out. To trace the path of the body harness, look at the BE section of the FSM.
If my instructions don't make sense, send me a PM with your phone number. Sometimes I can explain this over the phone more easily than I can type it up.