It is a switch. When the brake pedal is at rest in the upwardmost position, the unnumbered little button above the spring in the picture depresses the switch. When you depress the brake pedal, the switch closes, turning on the brake lights. From everything you're saying, it's the switch that's bad. It could be the hazard switch, but usually that's accompanied by erratic turn signals...

Fasteddy's advice is occasionally sound...