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So this one is weird: The center brake light stays on after the car is turned off. The four other lights turn off, but the center one stays on... Stranger than that - it goes off after about 2 hours.
All of the brake lights work normally when the car is on.
Start by replacing the brake light switch. It's at the base of the steering column just in fron tof the brake pedal. You will need to remove the plastic hush panel in the footwell to get to it.
The 3rd brake light has a separate light blue wire coming off the switch and it's possible that the slide in the switch is sticking to where the brake lights go out but the 3rd brake light stays on until the slide moves far enough to break that circuit (I think its spring loaded).
The brake lights work without the ignition being turned on so a sticky switch is a possibility.
The third light is powered directly from the brake pedal switch. The power for the rear brake lights must pass through the turn signal switch along the way. If the brake pedal switch was to blame, then the problem would affect all of the lights, (and turning the ignition switch off would have no effect). There, that's a start.