Hyundai Repair Questions? Ask a Mechanic for Answers ASAP
What is the year and model of your Hyundai?
It is more likely that the brake lights are staying on than the tail lights. Does the third light stay on as well?
If it does reach up on the shaft of the brake pedal and see if the switch there is knocked out of position. If the switch is intact unplug it to see if the lights go out. If they do look at the plunger on the switch and see that it is pushed all the way into the switch when the brake pedl is up. If it is replace the switch.
let me know what questions you have and what you see.