...
without the motors and gears working the seats will not move period.
Unless they are forced and break in some way. My older 91 Lincoln would not move front to back, but in hard braking sometimes, it would slide forward from my weight(belted in). I think someone forced it in some way before. To move it back I just pushed it with my legs while sitting. I swapped that seat out years ago, I need to remember that the seat track is bad in that old one.
Seat track motors are made in sets, all three together R&R from the seat track.
Sorry, I missed that this OP has a Limited, the memory seat motors are special for that. Those motor sets have an extra electrical connector going into them, it's a set of position sensors. You have to find that memory seat motor set, which may match a few other seat models(Aviator or other years etc).
For non memory seat vehicles, the good news is that most motor sets can swap to either side. So for others people, find one from a passenger seat that has less usage, and it should last the life of the vehicle.
In the picture below, of my 99 Limited seat track, see the word "Memory" printed on the label. To the right of that, at the right corner of the motor assembly, there is a connector receptacle, a group of smaller gauge wires plug in there.