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Do you know which color wire is supplying the power to the light? This would help diagnosis the issue. So I'd pull one of the plugs and see which wire has the power on it.
But assuming the power is coming in on the brown wire... I'd check the brown wire at the front to rear harness connector on the forward side for power first. The power to the tail lamps comes from the headlamp switch on the brown wire and it's easily found behind the driver side kick panel. If you have power on this wire then you probably have a switch or switch ground issue. The headlamp switch has a grounding ring on it that grounds the switch to the speedo housing. (shown below)
If the power is coming in on the green and yellow, then I'd go to the turn signal switch connector and check the connection at the turn signal switch and make sure it's ok, then I'd check the brake lamp switch and see if maybe it hasn't malfunctioned and as Alan stated above, check the grounds at the lamps themselves.
This issue could be a ground issue, it could also be a turn signal switch issue or it could be a defective headlamp switch (or headlamp switch ground) issue.
-Willcox
Last edited by Willcox Corvette; Apr 5, 2017 at 12:41 PM.