I agree, almost certainly a ground problem.
One possibility, tho not by any means the only one, is the bulb holders at the rear. The original holders were a lousy design : the ground path is through two dissimilar metals held in contact only by the plastic shell. When the shell distorts with time, the brass finger is no longer in good contact with the steel spring and the result is no ground connection.
Current replacement bulb holders (from the usual suspects) are redesigned with a separate ground tab. Requires a little extra work to install (you have to fabricate the ground wire), but solves the problem forever.