My immediate guess would be that you have a ground fault in the lighting circuit,
probably in the brake lights, probably caused by corrosion.

Since all the lights are generally grounded either directly to the car's metalwork,
or to the light cluster which is then connected to the body, if the ground connection
fails or goes high-resistance odd things happen. For instance, indicators on makes
one brake light flash dimly, or something like that.

Check that all the bulb sockets have the ground (outer) connected to the
bodywork with a multimeter. This should ideally be done with any bulb-holders
in place, rather than removed from the car.

Another possibility I just thought of, although I don't think it's likely: Does your car
have a brake-pad wear indicator lamp? Quite a lot of cars have sensors in the
brake pads, basically just a brass stud that is exposed when the pad wears down
enough, and connects to ground via the brake disc. I have seen some funny things
happen if this sensor wire is intermittently shorting, as can happen if it rubs on the
rotating components.

Pca