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I just upgraded my truck to 12volt. No wiring changes were made as I used the reproduction 6volt that I bought several years ago. I replaced all wiring from headlights to taillights. I replaced all 6volt bulbs with 12v. Now every time I push brake pedal there is no brake lights and when I push brake with headlights on the headlights dim a bit and the dash lights go out and the brake/tail lights go out but have a faint flicker.
The two things I would look at firs are grounds (if things act weird it is usually a ground problem). If they are OK I would check for shorts in the Brake power supply wire. When you changed from 6V to 12V did you change from positive to negative ground?