There are two adjustments on the steering gear box but GM had very little trouble with them. If you tighten them when it is not needed the steering wheel will bind as it comes back to center, and if you hold it centered it will want to pop off to one side whenever you hit a small bump in the road. It will be very miserable to drive and will feel the same as steering wander. You can identify gear box play by watching the pitman arm when a helper turns the steering wheel back and forth between about the 10: 00 and 2: 00 clock positions. The pitman arm must respond as soon as the steering shaft starts to turn.
While you're there, watch the ball and socket between the pitman arm and center link. Those often developed sideways play resulting in horrendous steering wander.
What is the symptom? If you can turn the steering wheel quite a bit before the wheels start to turn, suspect worn steering and suspension parts. Sloppy tie rod ends were real common. Worn idler arms were also real common. If you crawl underneath and tug it up and down, it should not move. If it does you will see the right wheel turn left and right and that will cause steering wander.
Steering wander can also be caused by not enough "caster". That is one of the three main alignment angles. Beginning in the mid '60s they began increasing caster to increase stability and reduce steering wander at highway speeds. Increased caster causes increased steering effort so power steering was added to overcome that. An alignment printout will show the caster for both front wheels and if it's lower than specs. The clue is no worn steering or suspension parts will be found and the wheels will respond as soon as the steering wheel is turned.