Third brake light has no voltage

[RyanS]

no, you traced the ground and power with a meter? checked for continuity?

Yes

 

[Doubeleive]

Yes

I suppose it's possible it could have burnt that part of the bcm then, nothing reprogramming would fix. you would have to replace it and the replacement would have to be programmed. it can be used it just has to be the same part number and learned to your vin
probably cheap and easy to just patch it in to the left or right brake light, if the ground is good all you need is 1 wire.