So I pull about open the casing on the Run/Off & Start button. And I naturally drop the little screw that holds the wire to the top casing into the bottom half of the casing and under the handle bar. Typical me. But if I grab that wire and push down or pull towards me the brake light kicks on. Pull up or away has no effect.

 

You are probably disturbing the brake light switch in the housing when you pull the wires.