on my 61 i had to take the tail light buckets out and sand them shiney, put in new grounding clips, get new mounting screws, and clean up the sheetmetal at the grounding points. I figured this out after doing alot of other work the turned out to be uneccesary but i sorted out some other gremlins in the process, so it was a mixed blessing. i would carefully clean and sand those parts and get new clips at least. they were like $1.50 for 12 and i only needed 4 i think. try that approach it is cheap and easy. it is almost certainly a grounding issue.
