Diesel starter, couple cranks then disengages from ring gear

Working on my MF396 with a 1006-6 Perkins.
I have an issue where the engine will fire and disengage the drive. If trying to start cold it takes forever, as you have to let the starter stop spinning to try again. The bendix is engaged by the solenoid through a lever (I'm sure pretty common).
I feel dumb, and can't just accept that the starter is no good. I've had it apart, and cleaned, no evidence of any issues. I have a new Agco solenoid which I bought well in the past, unfortunately, the lever mechanism on this reman is slightly different and won't attach to the solenoid correctly. Logically the only thing I can think of is that the electro-magnet is getting weak and won't hold the drive engaged through a complete start-up. For the brief time it does crank, it's cranking speed seems to be normal. I can eat the cost of the replacement, not the unknowing.
Thanks for any ideas

The solenoid has two windings. The pull in winding and hold-in winding. Sounds like the hold-in winding might be weak or the circuit open. You can test the continuity of both windings with your ohm meter. Specs will be hard to locate, but you can just compare the difference. The hold-in winding will have about three times more resistance. The hold-in winding might have lost its ground. You may be able to see the ground connection with the solenoid removed. Here is a picture of what I’m talking about.

That's a great lead, thanks. Something like that makes sense to me. I'll have a go at it with a multimeter. I should have enough parts to make something work out of this. I have some old starter cores from the tractor, unfortunately the current one is a Wilson and for some reason uses a different style plunger to drive the bendix. It's worth a couple hours of my time to save 350 bucks.

Would check starter drive. Have seen slip. Is sprage type locks one way slips other. A little wear and will turn engine over until a little resistance and then slip starter free wheels

Checked out the solenoid coil, ended up being the drive clutch in the end. Had one on a core that swapped in. Funny, a drive from the first core I tried wouldn't fit properly. Makes me wonder how they overhaul this stuff. Bins full of parts and try them till they fit? Doesn't seem practical to break down, clean and rebuild them one at a time. All three starters I have were from that tractor.
Thanks for the help,
Cheers