why don't the rear brake lights on my car go off?

check to see if your brake light switch is stuck

towards the top of the brake pedal is these cheap plastic stoppers that push in the plunger to turn off lights had same thing on Nissan pickup they just dry rotted away had to pull fuse to make lights go off till got my parts. would turn on park lights when coming to a stop was better than nothing

Agree with everybody! Also, switch is adjustable and may need adjusting so plunger is closer to the bracket on pedal arm.... Under dash! Replace or have the switch replaced if no problem found such as stated suggestions.

The brake light switch is located above the brake pedal, and as several of your respondents have answered, the brake light switch plunger touches a " cushion" which is made of a plastic that crumbles with age, ( you will find pieces of it on the floor mat ), resulting in the brake light always on condition. the light panel on the trunk panel is most likely a led design, and in most cases must be replaced as an assembly.

I had the exact same problem and found this video. I followed this guy's quick fix and it did the trick! https://www.youtube.com/watch?v=Gc9f5vk7ekw