Assuming it's a ground issue but here's what I'm working with. 1970 Cutlass Supreme. Installed a new light harness. Removed the old harness and noticed that two of the four ground wires were grounded to the front bumper brackets. My other cars all have the grounds going to the core support - two wires grounded on each side of the core support versus one to the core support on each side and one to the front bumper bracket. Is it possible that there is a ground issue and it would be impacting the rear lights? The rear brake lights work without issue - just not the tail lights themselves at night.

 

If the brake lights work then you don't have a rear ground issue in the rear. I would first check for power at the sockets, in front run a jumper for meter ground all the way to the battery if needed . If you don't have power there then check the corresponding fuse first.

 

I’ve never heard of any grounds on the bumper brackets on these cars. That’s just bizarre. Did you check assembly manuals.