Starter/flywheel

Sounds like it might have a bad solenoid. The problem is there's two coils of wire in it so if one is open, electrically it will test okay. The magnetic fields of both of them are needed together to pull the plunger into engagement and turn on the starter motor contacts. Each time the solenoid is energized the current flowing through the coils creates heat which can cause just enough distortion to prevent the plunger from moving freely. The cure would be a new solenoid but since the starter is under warranty, I'd get a replacement starter.

Rather than try to make it work, the goal is to keep it in the defective condition so you can diagnose it. Given that it works for a while when moving the starter, I'd be inclined to look for a corroded battery cable at the starter. To find that, connect a test light to that fat terminal. You can connect the test light's ground clip to that terminal, then connect the probe up on top of the engine where you can see it.

The light should be bright all the time. It will normally dim just a little during cranking because the battery voltage gets drawn down a little, but if you see the light go out completely, you know there's a bad connection. Then it becomes a matter of narrowing it down. The least confusing way is to start at the battery with the test light's ground clip and probe on the two terminal bolts. Have a helper try to crank the engine. If the light goes out, you have bad connections right there at the battery. If the light stays bright, move the clip from the negative terminal to the body and try again, then to the engine block and try again. Leave the clip on the engine block, then move the probe from the positive terminal to the starter. You're looking for the point at which the light goes out when trying to crank the engine.

All of this assumes the starter solenoid is kicking in with a fairly loud clunk. If it's not, head for the starter relay. We'll have to determine which measurements to take there. Feel if that relay is clicking when your helper tries to crank the engine.

Just proves I got another one fooled. I only know three things, and you asked about one of them, but if you feel like thinking I'm a genius, you just go right ahead and think that.

Gots my fingers and toes crossed!