Rainman and Map Tester: the picture that MT provided is a much better one than I could make. I just tried, and the quality just ain't there with my digital camera.
The switch is essentially encapsulated within the small plastic box. The little lever thing (and the plastic box, too) has a U-shaped notch that fits over the brake cable, and the screw traps the brake cable against the box. If you see how the plastic box is positioned, it is kind of trapped between the caliper on the brake itself and the cable end. Every time you pull on the brake, the switch is actuated by being compressed between those two points.