Taillightswillnotgooffunlessyoutakebatterycableoff

are the headlights off? if yes could be brk lights.unplug brk light switch and see if they go out

I had the same problem you are having with your corolla with mine. I'd turn off my car and take the keys put them in my pocket walk behind my car and BOOOM brake lights are ON... what the heck?? So, that turned my curiosity on and looked at my brake pedal.. what was going on? There is a problem in the pedal area under your steerin wheel, the brake light switch is not disengaging... what did I do to fix it? I jammed a glass coke cape in between the break light switch and brake pedal, and looked behind my car the lights were off.. its been 6 months and haven't had a problem with it so far.. Do you want to fix it correctly? I suggest you inspect the brake pedal spring and replace if needed.. or inspect the brake pedal button mechanism and replace..