Just be systematic in the diagnosis.
With the wheels on the ground have someone move the steering wheel back and forth.
While they are doing that start with the steering wheel to steering gearbox shaft and find where there is movement on the steering wheel side of a connection and none, or less, on the road wheel side of the connection.
It could be (probably is) any combination of:
Steering shaft u-joint loose on shaft or steering gearbox (least likely)
Internal play in steering gearbox (adjusting nut on top)
Loose pitman arm
Loose steering box mounting bolts (or any other loose bolts in the steering system)
Ball joints
Panhard rod fixings/bushings (Not directly connected to steering, but centralizes axle with chassis to prevent relative side to side movement)
Loose wheel bearings
Swivel pin preload
Other worn suspension bushings will contribute, as will worn tires.
Check everything in the list and make sure they are all up to par.
If the problem persists then you need to adjust the swivel pin preload. Consider a rebuild rather than just removing shims which is nearly always only a short term fix.