So the other day my brake light stopped working and I feel it is because it is not getting enough power. Bike is a '97 1200.

So far I have:
-connected light bulb straight to the battery and both filaments light up properly.
-the connector is only sending 11.7V to the light
-battery tests 12.3V and bike starts up as it should with no problems
-fuse is working as it should, all the headlights work normally

 

11.77 volts is enough to light up the brake and tail light more than bright enough. Is the running light working? If not I would check your ground wire as this would be the only common wire for both filaments. If it is just the brake light filament not working then I would suspect the brake light switch. Does it do the same thing with both front and rear brake applied one at a time? If it does not work with either one of them activated, I would suspect the brake hot wire that runs under the fender to the rear tail light assemble, it may have come loose from it's clip and damaged buy the tire when it travels up towards the fender when hitting bumps, dips and pot holes. Or it could be something as simple as the socket that the light plugs into. You might also try cleaning the connections at the rear brake switch, it sometimes gets a bit of gunk built up and may cause a partial, resistive short.