How far does the wheel move before the tires start to turn? Be sure to check every link. Wiggle the steering wheel and look at the output shaft
You should have about an inch of free-play before the wheels start moving, at least that's what I remember. Also, it's a good idea to purchase a vintage genuine Ford service manual for your car as it will answer many questions when it comes to servicing and maintenance, such as all the locations that need to be greased on a regular schedule.
Play can be compounded. There's a chain of connections from the steering gear to the wheels. There are the drag link tie rods, on and on to the king pins. Also, the bolts securing the steering gear to the frame. This why you need the manual. Do the checks. Be aware that the steering gear adjustment is only for so far. Many repairable steering gears have been ruined by cranking down on the adjustment nut. The primary purpose of the adjustment is to set pre-load. Too much and it starts to destroy the worm gear. This makes the gear harder to turn and gives the illusion of tighter steering when in reality, it's still a worn box. The true way to adjust early Ford boxes is by shims. In other words, overhauling the box. Before I pulled the box, I would double check the steering system per the manual as listed above. There's a big troubleshooting list.... Lastly, These cars are 75 years old. Cars drove differently then. They would have a slight wonder. You have to drive a 75 year old car, not ride in it. See how it drives. They drive well but they are not like a new Camry.
The first thing you need to do is a systematic inspection of your steering and suspension components. Get a helper who can follow instructions. Jack up the front end and grab each tire top and bottom and wiggle in and out. If you can see motion between the brake drum and backing plate it's probably loose wheel bearings. If you see play between the steering knuckle and axle it's king pins. Park the car on level ground. (A drive on lift makes things a whole lot easier.) Have your helper wiggle the steering wheel back and forth. What you are looking for is play in all the steering joints. Start at the steering box. Does the input shaft move without corresponding movement of the pitman arm? Does the drag link move with no play between it and the pitman arm? Does the right side steering knuckle move with no play between it and the drag link? Does the right side tie rod move with no play between it and the steering knuckle? Does the left knuckle move with no play between it and the tie rod? Check both ends of the panhard bar for play. Check the spring shackle bushings and the spring to frame mounting bolts for play or looseness. Check the wishbone mounting points. Before making an adjustment on the sector shaft backlash grab the input shaft and tug up and down it make sure there isn't any play in it.
My "M-word" steering box had, what I thought too much play. One of my car buddies suggested check to see if it had grease in it. It's right by the exhaust headers and over the years had cooked to grease out (I guess!) I pumped in nearly a whole tube of grease in it. I just used the water proof bearing grease because that's what I had. It steers like a brand new M-word! Was that the 'correct' type of grease?.......I doubt it! My way of thinking.......any grease is better than no grease. It's been working great for YEARS! YRMV 6sally6
Those steering boxes are not hard to overhaul. Try adjusting it by following the proper adjustment procedure. First, check for play in the worm bearings. If you can detect any up/down movement in the steering wheel when turning it back and forth with the wheels on the ground you can remove the square bottom plate and remove one shim. Reassemble and try it. You will have it right when you have 2 -3 pounds of turning resistance at the steering wheel rim with the wheels off the ground. Next, with wheels off the ground, turn the steering wheel lock to lock and count the turns. Divide that number by 2 to find the high spot on the sector. Have someone hold the wheel in that position while you loosen the adjuster lock nut and turn the screw in until just snug and tighten the nut while holding the screw. Lower the car and check the free play. If it's still over an inch by much you have worn parts somewhere in the system, i.e. sector shaft bushing, tie rod or drag link ends, king pins, loose wheel bearings, etc. The tie rod on these has one end that is not replaceable. If that end is worn, you need to find a new, or better, tie rod. These old steering boxes require 90 weight gear oil. When the sector seal goes bad folks would pump it full of chassis grease to eliminate thee leak problem. Bad idea! Replace a leaking seal.