I'm in the process of rebuilding mine(Farmall 100, same tractor). Mine had over a 1/4 turn of slop, plus it would shimmy at higher speeds. My governor is re-worked and the tractor will get into the high teens(mph) so it gets scary. The cause of the shimmy may be something else(toe in/out), but the loose steering isn't helping.
First get the complete service info for your's at Binder Books. Order a rebuild kit. The kit should consist of bearings bushings and gasket. If you need further parts you'll know after getting it apart. My sector gear has wear, but not enough for me to purchase one of those Chinese knock off "cast" gear sets. You can also have the original gear rebuilt if needed. Friend of mine pinned the sector gear to the sector(pic below). It uses a woodruff key. The key wears as does the gear to sector fit. Creating slop. Also I found my sector bearing worn. It allowed about an 1/8" up/down movement of the sector shaft.
I've researched this pretty thoroughly. Another area that can cause loose steering is the pitman arm to sector shaft fit. It also uses a woodruff key but the shaft is tapered for a tight fit. If the nut comes loose, it will allow the pitman arm to walk. There is a bronze bushing in the low steering case. Mines tight, but they've also been known to wear allowing side to side movement. Also, you'll find most folks install a zerk fitting and grease the steering gear assembly, instead of using gear lube(which leaks regardless). Another thing I'll be doing is shimming the bearings to try and tighten the "feel" up some. Above all else, get it apart and checked. If the sector gear woodruff key is the cause, it has been known to sheer, causing a multitude of damage to you and property.