With the car on the ground and the wheels going straight. Have someone get it the car and move the steering wheel from center to the right and left where the play is. Just bump it into where it gets hard in both directions. Have them keep doing this while you get under the car and inspect the following for what looks to be movement.
Check the steering wheel to make sure it is tight
The steering box mount to the bracket and to the frame
Play in the steering box gears
The pitman arm
All drag links
King pins
The spring perch bolts where they go through the axle. Look for a ring of rust on the top of the axle, this indicates it's lose and moving.
Even lose backing plates are wheel bearing could cause loose steering.
I bought a 40 coupe years ago and the steering wheel had at least a 1/2 turn of slop.
Almost everyone of the above bolt on items was lose. All were tightened with NO PARTS replaced and the steering had no play when done. G.M.