Ah…. California Special taillights…… What fun…
Amy’s car had two problems. The brake light switch and the headlight switch. The halogen headlights do increase the load on the headlight switch. Satan’s was old and its failure turned off a lot of stuff. Her taillights were an easy fix for a young person who loves to contort himself or herself under the dash…. Simple brake light switch replacement fixed Amy’s problem. Yours is bigger IMO.
The first thing I would do is find the ground wire for the taillights. They are mounted in fiberglass and the ground wire is critical. With the trunk open look down the right side of the frame that surrounds the trunk lock mechanism on the inside of the trunk. There should be a small screw holding two black wires. Make sure that the metal is shiny and the wires are not broken loose from the clip that the screw attaches them to the frame.
Take both lenses off. Makes sure one side has not lost its reflective capability. More than the other. 4 screws for the outer ring and 4 screws for the lens.
My guess, from the keyboard, is that you turn signal switch is failing. I have seen a lot of people chase the harness from the back to under the dash, and into other areas. This is where Amy’s suggestion is a good one. Neil (franklinair) turned me onto the new LED taillight bulbs. They draw far less “current” than the traditional 1157 bulb. The turn signal switch carries the load of the taillight and brake light filament. The turn signal switch was designed to hold the draw of two taillights, not 6. It is my opinion that this leads to turn signal switch failure on our cars. Replacing it is fun, but we can step you through it.
Digest the above. Steve Wick, (rvrtrash) is the expert. He may have some other simple things to check.
Rob