Run a separate ground wire to one of the light sockets, the tail lights ground out thru the mounting hardware on the tail lights. After 50+ years the connection isn't what it used to be. And it wasn't that great a design to begin with!
I have had the issue on many GM cars built in the 60's & 70's.
Also check the sockets connectors for corrosion. Sometimes the spring tabs on the bottom lose contact with the tabs on the bottom of the bulbs. I have also soldered some larger globs on the bottom of the bulbs to make up for the lose of spring tension.
If that the case the sockets are really worn out. And should be replaced. The tail light harness is not hard to replace and usually runs around $120 last I checked. But that was many years ago.
Good luck