It definitely can be put on wrong, and they do go bad. Take the switch off, plug the wiring back into the switch, and then take your finger and press on the switch through the hole and see if the brake lights work. Doing this you will also see how it works. The rod from the booster has a very large sloppy hole in it. Much larger than the pin on the brake pedal arm. When the switch is installed, and the pedal is slowly pushed, the booster rod doesn't move, because it's taking up all the slop between the pedal pin and the booster rod hole. When it does this, the end of the booster rod starts pushing on the brake switch, closing it. When finally all the slop is taken up between the pin and the booster rod hole, the pin will start pushing on the booster and applying the brakes.

 

I was just about to post in my thread that I got it. details there, but thanks again