There are a couple of things that may be biting you. The most likely is the switch itself. The next is the rear limit switch that prevents rearward motion if the seat is already all the way back (even if it's not!). Since you'll be in there jumpering things to get the seat back, you'll quickly find out which it is.
To get the ground side, you will need to short pins 3 (white/black wire) of the seat switch, and 2 (blue/black wire) of the seat switch. To get the +12, you will concurrently need to short pins 16 (blue wire) and 4 (brown wire).
Relevant bit of the schematic attached.
IF the aren't any issues with the rear limiter switch, the seat should move back for you. If it doesn't, you'll want to ohm out that switch between ground and pin 2 of the seat switch for continuity.
I have a similar problem. 06 Santa Fe with 8 way seat adjustment switches. The seat goes forward and back, the seat height adjustment to the rear goes up and down, but the seat height adjustment to the front does not work at all and the seat back will only go forward and will not recline. The seat back reclining problem is the most important issue as it is all the way forward and now awkward to drive. Any advice from anyone would be greatly appreciated. Thanks.
Since the seat back can move forwards but not back, I feel pretty certain that is going to be a switch fault. You could remove the switch and bypass it to recline the seat until you get a replacement if it would make driving easier
I posted pic and the location of the limit switch which was stuck. Save having to pull out the seat as I did to release it. Search for it and save time. Mine was a white actuator at the rear right side of the drivers seat.
I think Chris has the earlier model that has a different switch to what's shown in the attachment.
A quick Google search turned up the correct schematic for the earlier model. The recline motor wires are Blue/Yellow & Blue/Red. Apply 12V to one wire & ground the other should make the seat back move one direction. Reversing the 12V & ground should make the seat back move in the opposite direction.
Only Hyundai, knowone else have that problem. I almost couldn't drive the SF. Got squeezed out too far forward but lowering it gave me a reprieve. Then I fixed it and the switch it self is the issue nothing else.