One problem related to turn signal has been reported for the 2004 Hyundai Tiburon. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2004 Hyundai Tiburon based on all problems reported for the 2004 Tiburon.
Right turn signal stays constantly glowing out of no where. Turned the left signal on and the right signal came on as well and stays on even when the car is off. It doesn't blink it just stays glowing. I have read numerous reports from mechanics and other driver with the same vehicle that the relay inside the bcm tends to go bad. If it were just a fluke and it was just mine that was bad I would cough up the money and replace it but if I find numerous people that have had the same problem then seems like Hyundai has a faulty part and it needs to be fixed, and also funny how if you order the module on the circuit board that needs to be replaced the part number has changed because they have updated that module so they must have even found a problem with the module. Seems like a safety problem as it confuses drivers around me because my right turn signal is constantly glowing then all the sudden left turn signal is flashing.