parking lights still working. signal lights still working.
I don't know why these people think it is a fuse when the third light still works. The car manufacturer would not spend the money to put extra wiring and a fuse if they didn't need to. I will go with the wrong bulbs, that can happen but it is not likely you blew both bulbs at the same time. You have power from the switch and that goes to the turn signal switch then to the rear lights. You have either lost the power to the turn signal switch or lost it is the turn signal switch.
certain vehicles like late model jeep grand cherokee's have small printed circuit boards in the tail lamp assembly that are not serviced and i have seen both go bad at the same time. don't know what you drive but there is some info for you. check for the presence of a signal during brake application at the plug to the tail light. if you have a power supply when on the brake, and a good ground than it can only be the bulb or a PCB in the lamp assembly that is bad.
consistently attempt the least complicated element first. it isn't any longer remarkable the two bulbs failing close jointly. they're the comparable age in spite of each and everything. purchase one bulb to be sure. At worst you will have a spare bulb! freshen up the bulb holder contacts with WD40. Then examine the brake mild change that's ordinarily decrease than the pedal. it is displaced or % changing. you could attempt the circuit by ability of circumventing the change for the time of it is contacts with the ignition directly to work out if the brake lighting fixtures fixtures perform. After that it is a fractured twine which will % an vehicle electrician to discover.
I would say chekc the wiring that branches to both lights. Not the fuse.....
Sounds like it's a fuse. Exact same problem with my F-150. Until you're able to buy a fuse and replace it, just keep switching to the parking lights every time you brake, may get annoying, but it's better than unexpectedly getting rear-ended.