Car tail light burning with all switches put to off. Ultimately, I had to remove the battery

Just had this issue myself on my 1998 Sonata. I discovered that the brake light button (for lack of a better name) had deteriorated and broken apart and fallen off. The button is located on the brake pedal arm under the dash directly opposite the brake light switch. The button is what actually presses against the switch to depress it and turn on the brake lights when the brake pedal is not depressed. If the button has cracked and either completely on partly fallen off there is nothing to push against the switch to depress it to turn off the lights. If this has happened recently you will likely find pieces of the button on the floor beneath the brake pedal.

I fixed this problem myself using a clothes button of the similar thickness (actually i used two buttons as I'll explain). The button is attached to a metal plate that extends out from the brake pedal opposite the switch. There is a hole in the middle of the plate (the orginal button had a stem on the back that seated the button and held it in place. I used a piece of wire feed through the button I was using to work with the switch and would be mount on the face of the plate. I gave the wire one twist to hold it snuggly to the button. I feed the wire through the hole in the plate. I then used the second button on the backside of the plate to hold the front button in place. I did this by feeding the wire through the holes in the second button and twisting the wire to hold it in place.

I do not know the actual part name for this button and todate have not been able to locate a replacement button. Just had this issue myself on my 1998 Sonata. I discovered that the brake light button (for lack of a better name) had deteriorated and broken apart and fallen off. The button is located on the brake pedal arm under the dash directly opposite the brake light switch. The button is what actually presses against the switch to depress it and turn on the brake lights when the brake pedal is not depressed. If the button has cracked and either completely on partly fallen off there is nothing to push against the switch to depress it to turn off the lights. If this has happened recently you will likely find pieces of the button on the floor beneath the brake pedal. I fixed this problem myself using a clothes button of the similar thickness (actually i used two buttons as I'll explain). The button is attached to a metal plate that extends out from the brake pedal opposite the switch. There is a hole in the middle of the plate (the orginal button had a stem on the back that seated the button and held it in place. I used a piece of wire feed through the button I was using to work with the switch and would be mount on the face of the plate. I gave the wire one twist to hold it snuggly to the button. I feed the wire through the hole in the plate. I then used the second button on the backside of the plate to hold the front button in place. I did this by feeding the wire through the holes in the second button and twisting the wire to hold it in place. I do not know the actual part name for this button and todate have not been able to locate a replacement button.