The brake lever also has a little pin going through from the lever side to the switch. The switch is "push for off" so when brake lever is released the pin presses on the switch and the brake light goes off, when you release the pressure on the switch it should turn on, BUT, the only pressure exerted to push the actuator pin back is the puny little spring in the switch, so if the pin is corroded it ain't gonna shift. Likewise, there is sometimes enough play in the mounting screws to keep the switch too close to the pin so it can't release.
I replaced my switch yesterday because in my case it was the switch that failed, mine came on a spare master cylinder off eBay, bargain if the switch costs 40-50 quid and you get a free master cylinder.