I wish i could just post a video but if you start to turn the wheel one way left or right it will continue all the way to lock with little to no effort
Best description yet. You start to turn and it's like the steering system/truck takes over and finishes the turn for you. Still doesn't jive with the statement of, "the steering wheel moves when you give it gas". Are you saying when you start a turn, left or right, and it feels like the system finishes for you, you also are in the process of giving it gas/accel? Is it different if you are sitting still and not moving and you turn left or right?
It may be a PITA, with all these questions, but without being there, we need to get it straight in our minds exactly what you are doing when you get this sensation of the steering system finishing the turn for you.
There were some trucks/steering systems that had steering assist for when you were at idle and turning and not moving. That is hardest on a steering system. Had some valving in the power steering pump and if you go with your guess of the steering gear, that is a lot of money for a quality gear box and the labor to do it and not fix the problem. I also asked if you had recent work done because if the alignment caster is off far enough, that can give a strange sensation when turning.