The repair was not hard so, for future reference, here's a quick rundown. There's a cover on the underside of the lever that comes off with phillips screws.
Inside is a small switch (see pic) that cuts off power to the motor when the brake is applied. I popped off the cover of the switch housing with my fingernail, exposing two terminals for the wire. On the back side of the switch housing is a strain relief, that I twisted off in order to feed the cable back through.
I had a friend with superior soldering skills solder the two wires back on to the switch terminals (very fine). I tested the switch to verify that it was working properly, before replacing the strain relief and the switch cover, popping the switch back into its slot in the lever and replacing the cover.
The only thing that threw me for a minute during the testing was that the switch allows the motor to run when it is depressed (brake lever keeps the switch down) and it cuts power when it is off (brake lever is pulled). This was counterintuitive to me but I figured it out pretty quickly. Otherwise it was an easy fix.