There rack shouldn't be where you get any play, that would be in the tie rods, I can't remember if these had idler arms or pitman arms off the top of my head or if they were a straight through just have a bar coming out each end of the rack going to the knuckles.
To check for play, raise the front end so both tires are in the air, grab the drivers side tire on the left and right and turn the wheel by hand just a little each direction, if there's any play it would move without the passenger side mirroring it, if they move together immediately, the connections between them are most likely all good, if not you just watch and see where the movement stops, look At the tie rod on that side, then follow it across could be something as simple as a ball joint. Should mirror all movement small and rear.
While your down there, check rotating top to bottom on both sides the same way as the steering, it shouldn't rock up or down unless your hubs have started to go bad. These tend to become more noisy than be felt in steering.
You can also check the sway end links to see if there's any play in them, but not likely your issue if it's only doing it while turning not just a bumpy road, would only click when bumps making left to right wheels when compared to the frame/body vertically uneven.
Random thought but your 22" wheels are hubcentric, right? I think these years where hub-centric, not lug-centric. That can cause some issues also.
Also since the pulling followed the tires it is probably just the tires, the roadforce being off(belt broke or stretched inside rubber) or the tires being feathered badly could cause that. New tire balancing machines can even tell the installer to rotate the tires on the wheel to lower it and make it the best possible ride.