Boland01

I recently purchased a 2010 535ix from a private party. My wife noticed the third (high brake lamp) would not come on when I applied the brakes. I took the cover off the third brake light and noticed the plug in was disconnected. When I plugged it back together the third brake light came and remained on even when the brakes were not applied.
Not wanting to run my battery down I unplugged the connection again. Does anyone have any idea how I can track problem this down? It seems the third brake light is not wired to the rear brake llights.
Does anyone have a wiring schematic so I can trace it back?
Could the third brake light itself be bad (I'm thinking that's probably not the culprit since it lit up when I reconnected the plug in cables).
Would the brake switch be a likely source or does it sound like a module or grounding issue.
Any directional help is appreciated. So far my interent search hasn't turned up anything.