I'm not real happy with your connection on the red wire or the ground. Just an instant loss of contact and that solenoid can drop out.I'll have to check tonight.
I didn't follow all of that, but I think I got the gist. I'm testing with the voltmeter on the bracket of the solenoid which is attached to the block, which is where the ground wire for the solenoid is attached.
I should bench test both solenoids, and I think I've done that, but it's been so long with so much testing I can't remember.
It's PULL to run, so if I hold it in that position it runs fine.
This is the tricky part. Both solenoids (old and new) cut off when they still have 12 volts to them.
So what I understand from you guys is that the black wire is ground, red wire is "hold" and white is "pull." So the white only gets 12 volts for a very short time at startup. Red seems to stay hot when the motor is running. I assuming this red wire is what keeps the solenoid open while running? I've attached a photo so you can see what we're talking about.
Also, does that linkage let the solenoid absolutely, completely retract when energized?