My "71" 350 with auto transmission keeps blowing a fuse every time I shift into or through reverse.  I thought it may have been a short in the rear backup lights as the sockets were in poor condition.  I replaced all tail and reverse light sockets, pigtails and grounds.  My tail, brake and turn signals work fine but the reverse light problem persists. When I unplug the reverse light circuit at the console the fuse does not blow so I figure there may be a short in the reverse lights behind that point.  Has anyone had this problem?  Is it possible that the contacts on the shift lever could be bad/shorting.  How would you trouble shoot this?  Many posts address the typical problems with their tail lights not working or working all the time but not blowing fuses.  Pretty obvious its a short somewhere but how to find it?

Definitely a short in the harness. From the neutral safety switch, the light green wire goes to the rear bulkhead connector, and from there, out to the two reverse lights. If you can get to the bulkhead connector, unplug it, and see if the fuse still pops in rev. If it does, the problem is somewhere between the reverse light switch, and the bulkhead connector. If it does NOT blow, the problem is between the bulkhead connector, and one(or both) of the bulb sockets.
Most likely is that there is a short in that harness inside the cockpit. You would need to trace the light green wire from the switch to the bulkhead connector to find the problem.
Or....put in a higher amp fuse, and follow the smoke...
(not really...)

Thanks Joel. The short is probably between the switch on the shifter and the bulkhead connector.  I just replaced all of the taillight and backup light sockets and wiring.  I was having the problem before I did this thinking it was probably corroded sockets.  I'll try to trace the wire tomorrow.

That connector will be in the far rear corner on the driver side. Kinda pain to get to....
Chances are the problem will be in the area behind the driver seat, where the wire harness runs from the center console area out to the door pillar.

Thanks again Joel.  Actually I found the connector near the fuse block under the left hand side of the dash. You have to be a bit of a contortionist to get to it. The pin had pulled out of the back of the connector.  Simple enough, but that shouldn't cause the fuse to blow right?  This is where things got interesting. Tracing back to the safety switch and out to the rear wiring harness I found that "Old Bubba" had patched in a jumper wire (using extension cord wire of course) from the Neutral Safety Switch down past the transmission and followed the frame back to the backup lights.  The jumper was worn through were it bent around the transmission support and caused the short.  It would have been much simpler to fix it right in the first place!  It's all good now!  Thanks for your advice.  I don't know where I would be without the forum!

Glad you got it taken care of!