Make sure to have a Fully charged Baterry, clean Pos and Gound cables real good..if this doesn't work .. jumper the pos to the solenoid to make sure its not the Starter you have just Installed..I have replaced many Bad..New Parts,,made in CHINA
X2. key switch and connectors would be standard procedure to check next. Always work cheap to expensive unless your 100% sure then skip ahead.Starters for those aren't cheap, i'd start with the solenoid first, since you got it to engage when you bypassed the solenoid.
Just my opinion
a friend of mine has a late 90s 6x4 gas gator And there isnt a good place to jump fromSo if you look at the starter it should have a battery pos wire to it and a small wire going to the solenoid..Take the solenoid wire off and jumper the connector/ small stud to the Pos cable...or leave the solenoid wire on ...I do not know how much room you have to Jumper it...You can do the same with the old starter with a pair of jumper cables