You should be able to feel the detents in the transmission even if the neutral safety switch is removed. A lot of the slop your feeling is probably due to plastic bushings in the linkage being worn out or plain missing.
The switch can be had at just about any local auto parts store. Easy fix but it requires a smidge of know how. It needs to be adjusted once it is installed.
It has been forever ago since I did one and you have to take a small drill bit to hold the switch in correct alignment when the transmission and selector on the column are in neutral and then tighten the screws that hold it in place. This adjustment is critical as you don't want the truck to start in anything other than Park or Neutral.