The prime suspect (other than possibly the combination switch) is the ground
on the brake/tail light assemblies. If the ground is bad on one side,
voltage will feed from the brake wire through the brake filament, find no
ground, then proceed backward through the tail light filament to the parking
light bus... causing the very symptoms you described. Removing the dual
filament tail/brake light bulbs is the quickest diagnostic - if the problem
continues, look elsewhere. If that cures it, replace one at a time until the
symptom returns, then fix the ground on that socket. If the symptom doesn't
return, one of the sockets is corroded enough to be intermittent.
Putting a single filament bulb in one of the dual sockets will always cause
this symptom, but if they haven't been touched look to the grounds.
Bingo, it was a bulb. Even though it was stil working, the filament holder
also, noticed that my positive battery cable was way corroded with sulphuric
acid. I cleaned it and put it back. Wonder why. The battery is only a year
old and I cleaned all contacts before installing it.
I forgot to mention - if there is a bad ground on one of the taillights,
turning on the parking lights and pressing the brake will cause the problem
light to go out since there will be battery on both sides of it and no
ground in the middle.
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