It sounds like you have a short somewhere.
yes they have brake lights and you probably have a bad brake light switch which is on top of the brake pedal under the dash.
open trunk and look behind the taillights as the bulbs just twist and pull out.
Are you blowing fuses or are the bulbs blowing? Blowing fuses would be a sign of any wires or metal contacts in your brake circuit grounding out or shorting on themselves. You'll have to check all of the wiring in your brake light/switch circuit to be sure.
check all brake bulbs a filiment may have shorted out
The # is 1157 bulbs.
It could be the brake light switch (the switch that activates the brake lights when you step on the brake pedal) has gone bad
check the fuse then the bulbs then the brake switch
Change brake light bulbs Just remove the rear license plate. You can change the backup lights and brake light easily.
It is possible that one of the bulbs is shorting out. Try replacing the brake light bulbs, if that doesn't work, troubleshoot the brake light switch.
You could have a bad brake light switch, bad bulbs, or a short in the wiring. Try changing the bulbs first. My Camry was doing the same thing. I put in new bulbs and no more problem.
Bulbs are replaced from rear of headlight. See answer to similar questions for how to do.
Check the fuse, check the bulbs, then check the brake light switch.