I've messed with those cables before, but I just can't pull an answer off the top of my head for you. Seems to me that you are going to have to pull the seat and get it onto a bench, & then pull the cover on the cushion up on the side where the cable is. That cable will go from the backrest to inside the cushion and the mechanism in there. Not sure where it will connect, but it should be kinda obvious once you get that cover up to expose the workings inside there. IIRC, it does have something to do with how the seat goes back & forth. I believe that there is a small connection on the end of that cable in a lazy 'S' shape. It should clip in somewhere on the cushion mechanism. Might even have a clip in there to hold the cable in the right position.
Tip. Take the bolts out of the front of the tracks first, where they bolt into the floor, then slide the seat forward to get at the back ones. This will help the seat to stay upright on the bench. If you do the back floor bolts first, the seat will want to fall over backwards, when it's on the bench. Then when you hit the release, those tracks will FLY backwards at finger removing speed! I still have all my digits, but you'll only do that once! How DO I know this? Hmmm...