I have worked on a lot of cars over the years and can't say I ever replaced just the solenoid. It may have been a problem while changing the starter but just replaced the whole deal.
Now, I have worked on tractors also and know that parts can be real expensive and or hard to locate.
Having said all that when I turn the key and just get a click or clicks first thing I check is battery, making sure it is not weak. I'm confused about jumping direct to solenoid.
But assuming battery is ok, next would be the brushes in the starter. As they wear down, the "brush holders" which are made of metal, can short against the stator where the brushes make contact. Sometimes this will cause a bad spot in stator and unit will function fine until it sits on that one spot.
Hope its an easy fix for ya, good luck.
For clarification, I am running a test lead from the hot wire to the post on the solenoid. Standing beside the tractor and starting it by "jumping" the solenoid.
I am attaching a battery charger to add amperage. Even when I add the battery charger set to 200a, it will not start with a key.
