I am a certified Hyundai technician and we see that problem all the time. Typically the fuel gauge problem is along side a check engine light but not always. This is a common problem for the fuel senders to go bad on these. These gas tanks have one fuel sender on the fuel pump under the driver rear seat and it has a fuel sender on a sending unit under the passenger rear seat. Replace both along with new locking rings and gaskets and be sure to install the fuel senders exactly how they came off. Disconnect the battery whenever working with fuel. Here is a guide and diagrams (below) to help you see what you are in for when doing the job. Also in rare cases I have seen the gauge itself go bad
Your car has a trap door so you don't need to remove the fuel tank.
Check out the diagrams (Below). Please let us know if you need anything else to get the problem fixed.
Images (Click to enlarge)
Saturday, April 4th, 2015 AT 6:15 AM