Otto - The brake light switch is located on the underside of the cab floor kick panel, pretty much directly under the steering column. Screenshots below are the switch info from the Shop Manual and a screengrab of a Denny Graham posted picture of his 1950 Chevy pickup engine compartment showing the actual switch and location.
Since the switch and wire connections are exposed to the elements, the switch and/or the wire connections do fail overtime. Repop switches are available from our usual vendors.

EDIT NOTE: It is a mechanical arm movement electric switch that is triggered by depressing the brake pedal. The brake pedal rod actual move the switch arm between the off/on positions. I've added a pic of the switch by itself from Jim Carters
EL106 ad page.