Tinkerer, I think the center of the solenoid in that video is a SS tube that holds the plain steel core that operates the valve.
Comet, I was explaining how the hydraulic pump works. That's all inside the hydraulic pump, the one in the video in front of the engine. I understand how the pump works, but explaining it is tougher. Trust me, it works, if you want to know how, just ask, or get the manual, it's more clear and has pictures. Don't take it apart
The gauge won't stay at 0 even with the destroke working, it will build SOME pressure. Maybe 200PSI, maybe 800, I don't know. It won't go to 2,500 or anywhere close if the destroke is working. Since you have the machine in running shape, and a pressure gauge hooked up already, the next time you use it, at low idle put 12V to that coil, and see what the pressure drops to. Just a split second, a couple times, will show what the needle drops to. Doesn't have to be perfect, it will either stay 2,500 and not drop at all, OR it will go way down.
Comet, where is the big ball bearing that you mentioned?
Also, what is the inside diameter of that coil? the size of the round hole in the metal bracket. If you have a drill bit set, see which one fit's through there easily BY HAND only. Also, what is the height of the plastic coil, or the inside of the metal bracket that it fits in. There are plenty of coils floating around that would work, but lets see what's happening first.