Unusual brake light problem

Might be a ground problem in the housing, socket or bulb. Sounds like a switch problem, though.

sounds like the switch problems I had.

fwiw, the replacement on a 67 looks exactly like the $10 'help' section replacement. Not sure if 69 has a different style switch.

You say the voltage is fine.....if that means you tested for power at the brake light socket in the rear of the car and it had power when the brake pedal was depressed, then you have an odd problem. Brakes and turn use the same wires but get the signal from different sources.

Now, if there is no power to the rear light when the pedal is depressed, it could be as follows.

If it is like the '66, it is the turn signal switch, it is a bad switch.
The way the system is designed, the brake light circuit within the turn signal is a separate pin setup based on the position of the switch. You could remove the steering wheel and do some checking there and maybe see where the switch is failing. On the '66, it is a small spring type wire that makes contact for the brake lights.

Four ways will flash fast if a bulb is not working in the system, such as the one brake light not functioning properly.

I have also seen a new wiring harness with a wire pulled from a pin, causing one brake light not to function on a '66.

Glad you figured it out. I just solved a similar problem in a way that surprised me. My rear turn signals worked fine until I turned the lights on. Then, when the left signal was on it was extra bright, but the right tail light went completely out when the left one flashed. I also had intermittent battery drain problems. Searched everywhere for bad grounds, wires, etc., with no luck.

With some advice from a mechanic, I finally pulled all the bulbs out of the car and found an incorrect bulb in the left front parking light. It was some sort of slightly odd-shaped thing that a previous owner had put in that was similar to an 1157, but had a slightly shorter base. Changing it out fixed everything.