I have 1996 mercury mystique and both break lights are not working?

You should check all the bulbs and your wiring circuit for fuses outside the fuse box, such as in line fuses.

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Filaments on actual bulbs might be burned out, pull the socket out from the back of the tailights and do a visual check on the bulbs, replace if needed...

what you have is an improper bulb or bulbs. A local Wal-mart has a directory for selecting the right type of bulb or bulbs for your car

Same problem have someone check the ECM and the turn signal assembly voltage. The ECM is located by fuse box under dash and turn signal assembly is in the steering wheel. But they can check the voltage on both before replacing. Good luck

Check the fuse. If the lights blew they may very well have taken out the fuse as well.

open the trunk and remove the nuts that hold the lens in place push the lens out from the studs and remove assembly ...replace bulb and re-verse procedure for re- installation

The "multifunction switch" is bad. In the old days, this was called the turn signal switch. The brake light wiring for the two non functioning lights goes through this switch. Have your mechanic check the wiring into and out of this switch. It's in the steering column.
Charlie

Check the brake light fuse. The high mounted brake light (third brake light) is on a different circuit than the brake lights. Hope this helps.

Fuses, bulbs, breaklight switch.

If the driver's side tail light is working, it's not a fuse. Use a test light to check for power at the bulb holder. One terminal will be for tail light, the other for brake/turn light. If the is constant power for tail light, replace bulb. If no power, trace wiring from bulb holder to driver's side junction. Probable broken wire between the two tail lights.