What about the tail/marker light. If the brake lamp is good, the grounds should be ok. I don't have a print for your year, but I don't think there are left / right fuses for turn signals or back ups. Sounds more like broken or wet splices where the left and right sides split.
Take the assembly out, set parking brake, put the key in run, and put tranny in reverse and measure the voltage on the wires going to the back up light. Leave the lamp in place, and stick the red meter lead in the wires. I have found a sewing needle with a jumper lead works well. (it doesn't make as big a hole, cover with liquid tape when done, nail polish will work if you don't have liquid tape) Hopefully you will find approx 12 volts on one wire and 4 on the other. That indicates you have a poor ground. More than likely you will have 9 and 0.