The sensor on the Brake Master Cylinder is primarily to tell the cruise control system to go on standby - OFF position. I do not think this switch has any direct correlaton to the brake lights in back of the car.
It is a secondary safety switch to turn off the cruise control so that if either the pedal switch or the Brake Master Cyl switch fails, you still have a secondary switch to turn the cruise control on standby-off mode. Since you have it disconnected now, the only switch you have to disable the cruise control is on the foot pedal. If you are in cruise control mode and the foot pedal switch fails, you may panic because the engine will be pulling harder and harder as you keep braking harder and harder. Until you finally turn off the cruise control at the finger-buttons on/near the steering wheel. Nothing is telling the cruise control to go to standby-off.
If you have any doubt of this switch being faulty, especially if the inside is wet, replace it. There have been vehicle fires (due to electrical short circuits) associated with this component.
And, yes. It can be associated with blown fuses in the dashboard / cruise control fuses.