Hi Caretaker, have you checked on the info here?
http://www.hemanual.org/hyundai_elantra ... -1048.html
To get to info about ESC, you will find it in the brake section or click here:
http://www.hemanual.org/esc_electronic_ ... -1900.html
Then you will want to check the troubleshooting section for ESC or click here:
http://www.hemanual.org/troubleshooting-1910.html
To read any codes for the braking system and ESC, you need a scanner that can read C codes or chassis codes. You will need to spend around $150 or more for a reader that does chassis code reading. This is not a generic power trouble code. Basically without the code, you will be guessing as the ESC relays on the ABS system and your ESC light may be caused by a problem with the ABS system. I have one of these:
https://www.amazon.com/LAUNCH-Support-T ... B073GW5MTS It is probably the cheapest reader for C codes. I do not know remember if it will read any ESC coding but I do remember reading each of my wheel speed sensor speeds.
I have a '12 KIA Sorento and I know that KIA has a service bulletin out on the rear wheel speed sensors on the '11-'13 Sorento. If you get a DTC codes ranging from C1206 to C1211 it can be caused by water intrusion into the rear wheel speed sensor and the rear hub has to be changed. This is on the two wheel drive Sorento, which is the same basic drive train as the KIA Optima. I am not up on the Hyundai side of things but is the Elantra the sister model of the Optima? If you dig, you may find service bulletins for the Elantra.
ps Forgot to add that the Launch CPR-123 can read about any car make out there. It can be used on the Vibes too and your other cars. If you get one and want to use it on your Vibe, you have to select Toyota Matrix and it work fine. If you pick GM and the VIN number for the GM model, the Launch does not work. I have updated mine so it may work as a GM model now but I have not tried it. That is the other thing about the Launch is that it is up gradable with downloads over the internet. Newer car models get added with the updates. The only thing I would like different with the CPR-123 is that it would have a bigger screen, which you can get now if you spend more money.