Loose steering

So, if I understand you, you can hold the wheel steady but the truck will wander, but if you move the wheel to correct it there is a large amount of wheel movement before the steering actually corrects? If you set still and rotate the steering wheel left, how far do you need to move the wheel to the right before the tires actually start moving? Do both tires move at the same time or is one delayed? From the basic description it sounds like a worn steering box, but the above questions will help answer that. Another item would be the idler arm on the frame that carries the center link. No rack on that truck, it's a conventional steering box.
Bad tie rod ends would act differently. Sway bar won't do it either.
Easy enough to test though, have someone turn the steering wheel aback and forth a full turn each direction while you watch the steering box and pitman arm, then look at the idler arm on the other frame rail. I would also say that you will likely need an alignment as well as replacing any of those parts will change the settings.

Okay, if both tires are moving at the same time it is most likely the pitman or the steering box itself. If it was the idler one side would move and the other would take a bit as the slack in the idler was tightened up. Same if it was rod ends. Look at the box and it's mounting they have been known to crack the frame on some, not hard to repair just annoying to get into position for welding.