I have dealt with this issue on my trucks.First off I made sure beyond a doubt that I had good grounds on signal/parking lights.Next I pulled the bulbs out of the side marker lights to see if it made a difference.In my case it definately did,my side marker clearance lights work through a less than sufficient backfeed system that causes problems when the bulbs are plugged in...I assume it may be the same for '71 E-bodies but don't know.

Sounds mostly like you have a grounding issue somewhere since the problem is intermitent...perhaps this wiring diagram will be helpful.