Why would the brake lights go out in my 2003 Ford Mustang, when all of the fuses are still good?

Could be the stop light switch connected to the brake pedal.

if you installed an aftermarket stereo, the tail lights run through the illumination. make sure all wires are hooked hot to hot and ground to ground. if you installed it while battery was hooked up and touched a wire, most likely blew a fuse

check the brake light switch. Also check for a broken wire at the switch connector. The brake light switch is located on the brake pedal.

nutral park swich out of adustment or defective
brake light swith/ fuse/bulbs/wires to lights

If all those were good, they would work. Check fuses 33 and 41. You need to verfy if voltage is at the switch and going through the switch while pressing the brake pedal.

first try a new bulb on one side of the brake light at the rear if still not working then i suspect it will be the brake light switch assuming your fuses are all good.

pull out 1 fuse at a time and look at the wire trace inside if it looks broken or black, replace it. if it looks good. put it back in and keep trying

there is a switch located at the top of the brake pedal bracket that maybe bad.Check it for power on both sldes of the connector with a test light. Also try move it up and down to see if your brake lights come on. If not check fuses.

Fuse panel is under the dash also as I have found with my own graceful daughter, there is a brake light switch that connects to the brake pedal itself. It is hard to get to and even harder to see but a lot of times these switches get bumped and they can not make connection when the brake pedal is depressed. Hope this helps

Check the fuses, if they are blown, make sure they are the right size. If not, do not use bigger fuses than the circuit is supposed to have. If they are too small, use the correct size. If they are, do you have any extra equipment using the same circuit? Like a stereo or GPS or an alarm system? Move them to a different circuit. Check the relays to see if they are defective. Check all the bulbs to make sure they are the right ones too. Make sure they are in the right way. Check grounding wires, make sure they have good connections.