I agree with Dave, you have wire(s) broken inside it's insulation.
The wires will break where it flexes around the hinge.
You'll want to repair the break at the hinge.

You need to remove some trim to see the harness.
The harness is routed via the driver's side tailgate hinge.
You likely have a broken Brown/Black plus wire and/or a Black ground wire.
Tug and wiggle the wires while watching the center light to see which one or both need repair. Use high quality stranded wire for the replacement.

For good info to do wiring repair check www.davebarton.com
He has write-ups of the supplies and tools needed to do wiring repairs
He has a full line of parts and supplies.

Avoid cheesy crimp connectors, stick with high quality USA parts.
There's some ratty crimps on the market that are unreliable.

Good luck, Bill