My passenger rear brake light and turn signal work fine while my parking and driving lights are off but when I switch them on the passenger rear brake and turn signal light do not work ... What could be causing this ? I've replaced the bulbs .
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Easy stuff first; check fuses.
Then check wiring. Pay particular attention to the plug at the rear for the lights (not at the housings but under the bed). This is a common culprit for lots of odd problems. Look for bare wires, although they usually pop fuses.
Tail light circuit board? Notorious POS's.