Best way to check for movement is to have someone who can actually listen to instructions at the wheel. Ask them to move the wheel back and forth without putting too much force on it and not too fast, but back and forth at about one second intervals until resistance is felt (engine off, wheels on ground). While that person is doing that, you will be crawling underneath the car, looking for lost motion, starting at the universal joints on the steering column shaft, and working your way down. Listen for clicking and clacking too, but don't worry if there's a little click in the box when power is off, as long as there's not a lot of play. Make sure you look at the output (pitman) shaft of the steering box, which often develops side play. Check all the steering joints, and as the vehicle is slightly rocking, look for lost motion at the ends of the track bar. Basically, there should be no wobble, lost motion, play, etc. at any of those joints. A tiny bit of side play at the steering box may be acceptable, but more than a very small amount will give you sloppy steering.
If you are still looking for problems after that, jack up the vehicle by the axle tubes, just high enough to get a lever under each wheel. Then lever upward on a tire, and look for up-down motion at the ball joints. None is acceptable. Grab the wheel and rotate it, and check for any play in the bearings too. None is acceptable there either. It should be smooth and quiet, though a 4WD axle will not spin freely.
While you have the wheels up, crank the steering to full lock, and rotate a wheel. If it binds, or makes crunching noises, you have a bad axle universal joint. When bad enough, that can contribute to wobble when you're turning.
Finally, if you have death wobble, check alignment and wheel balance. If your wheels are well balanced and round and pointed the right way, it shouldn't wobble on the straights even if the steering is loose, although loose steering may be very sensitive to bumps. If your tires are nibbled and cupped, you'll have wobble no matter what you do to the front end. Try rotating tires and see if it changes.
