Yeah, I have replaced the solenoid with 3 Autozone ones in a row and they didn't work. Then I put on a junk yard one made by Ford and it worked fine. Some parts it doesn't make much of a difference who made them. But this one does. All that solenoid does is when you turn the key to "Start" it energizes the red/blue withe which energizes a little electromagnet inside the solenoid. That causes a big bar to slam into the 2 posts and complete the circuit to the starter to spin it. Whe you let off of the key, the electro magnet pulls the bar back down and breaks the circuit. and starter stops and backs out of the flywheel. If the starter stays engaged, it's because it has welded the bar to the posts and the circuit is closed because the electro magnet can't pull it back down. Reason is cheap solenoid.

The cheap shit can't stand up to the current. Get a Ford one. Get one like this, not that box looking Autozone thing in you picture...