Always make sure your tractor is in "NEUTRAL" when playing around a starter.
See if you have 12 volts at the starter, it could be the solenoid on the starter or the starter itself.
It could also be ignition switch related or poor connections to the starter.
There are ways to "bypass" the solenoid on the starter, I prefer not to show or tell you how for safety reasons.
You could also remove the starter and test it or have it tested.
Good luck.
I have starting Issues on my 574 model 1972, have a new battery, missing service manual, the starter won't kick in, only a click when I try to start it.
Anyone hve some good ideas what I might face ;-)