Well, if you say the switch works, did you test the switch out of the car or in the car? Did you test if you get voltage up until the switch?
Don't quote me on this, but I would say there is one wire going into the switch and one wire coming out, the one going in would be before (and probabally run to the fuse box), and the one going out would go to the brake light, if you test the one going in for voltage to a ground you should always have voltage, if you test after you should only have voltage if the brake is pressed.
If you get no voltage before then your fuse or your wire somewhere up until this point is broken
If you get no voltage after the switch but you do get it before then you switch is broken.
If you get it before and after then I would go and test right at the brake light to see if you get voltage when the brake is pressed (you shouldn't get any when the brake is not pressed)
If you do then maybe the brake light itself doesn't work? I'm not sure if they are bulbs or LEDs in this car I haven't taken that close of a look, if it is a bulb have you tried changing it? I am guessing that you mean all brake lights are out (I just checked and you said brake lights, so I'm guessing you mean center and sides if that is the case then I doubt they all burned out)
Weird problem
