On the subject of steering boxes.
Leaking seals is not the only thing that goes wrong with these 58 and up steering boxes. The main needle bearings that support the cross shaft also wear, and can actually break. The cross shaft and the piston housing which has the worm gear inside, do not wear that much. They are also adjusted to have a pre-load, and if properly adjusted are not the source of play in the wheel. There will normally be somewhat more pre-load on center that at the extreme left and right, because there is less stress on center than while steering. Most of the play problems with this system are where the column shaft attaches to the box by the rubber insulator. The insulators wear badly after 60 or so years of service, and get even worse if there is a leak in that area. There are also 2 plastic sliders that separate the rubber from the metal shaft to lessen friction. These also wear out.
With the way these steering boxes are designed, you are always going to have play in the wheel with the engine off. When you turn the wheel, a flexible disc moves and in turn moves a valve which controls the power distribution. What you feel with the engine off is the disc flexing. The response is immediate with the engine running. I have seen one instants of the disc cracking.
See your shop manual for even more in depth information.
Don Verity