One approach to consider: a simple micro switch that the brake cross-over rod compresses/releases to control the power to a modified tail light socket. Mount the switch on a simple L-bracket behind the transmission out of sight. (these are tiny, waterproof, under $15 USD and can be set ON/OFF or OFF/ON).
On my 1928 Henderson, I then purchased a common 2 contact socket (1157 style) from an auto and trailer parts supply shop which allows for running and stop light. It goes into the stock housing and is great with an LED bulb.
Of course, you will need to add additional wire from battery to switch and switch to stop light. Good luck!