One brake light doesn't work when head/parking lights are on. Ideas?

[Rust-O-Matic]

Hi guys, I just finished rewiring most of my '66 with the AAW factory style harnesses. I did the entire cab, under dash including new factory type fuse box, all new switches including turn signal switch inside the column, and all the harnesses that go from the firewall forward to the engine/sensors, etc. I also replaced all of the lights front and rear (housings, lenses, sockets, bezels, the whole shebang with new ones from Brothers Trucks).

I went to test my lights one at a time and the following stuff works:
headlights
parking lamps front & rear
turn signals left and right, front and rear
brake lights when the pedal is pushed
backup lights when the shifter is in reverse

The problem is....
When I turn the headlights (and/or parking lights) on, the passenger side brake light just goes black when I press the pedal. Driver side brake light works fine. With the head/parking lights still on, I turned on the turn signal and both sides work just fine.

Anybody have any idea what the hell to check here? Maybe a weird ground issue or something? Seems unlikely since they work the rest of the time. Since brake and turn use the same filament, I would think that if one works they both should. Also seems like if the brake lights both work with the headlights off, they should both work when they are turned on as well. I'm totally stumped.