For the last few months I've been getting the obnoxious brake alert and warnings on my dash every single time I hit my breaks. When I have the running lights and headlights switched off, the brake lights work fine but I still get the beep. Additionally, the front left amber bulb lights up anytime the brake pedal is depressed.

When I turn on the running lights or headlights, both tail lights and third brake light are lit, brighter than the normal running brightness. I took the carrier out of the tail light housing and the bottom light is constantly lit when the running/headlights are on. I also noticed that there is a wire that seems out of place. There is an end sticking out of the bulb housing but no sign of the rest of it in the wiring harness. Car has always been serviced at the dealer and I am friends with the previous owner who never altered anything. Pic included.

I'm wondering if anyone knows a fix, or if replacing the whole bulb housing should fix this problem? Any help is appreciated.