Welcome aboard.
I'm not familiar a C60, I have a C20, but wiring is pretty much the same. There are three wires to to the rear lights, turn signal right, left, and tail lights. The wires run from the firewall, a connector just above where the accelerator linkage comes through, down along the drives side of the frame to another connector about the where the spare tire is. The wire split at the the rear connector for right and left. In that the dumpbed is third party, can't say what was done, from the rear connector back. I'm also assuming that you have front turn signals so you don't need to check from turn signal to firewall.
Here's a link that should help;
http://www.64moneypit.pages.qpg.com/6066chevytrucks/id12.htmlLarry