1982 GPZ750 Starting issues

Spent some time last night checking the wiring and it seems my job might be a little easier than I thought. I was able to hook the battery up without it going crazy and left it alone for a few moments and it was still. I switched the ignition on and pressed the starter button. Nothing. I turned them both off and as I moved my fat body along the side of the bike, it began the whole starter craze. The solenoid was hanging out of the rubber holder and as soon as I touched the positive wire to remove it from the battery, it shifted the solenoid and the cranking stopped. I grabbed the solenoid and wiggled it and the cranking began again. Wiggled it some more and it stopped. I disconnected the battery, made sure all the connections elsewhere were tight (the solenoid in particular), hooked it back up and was able to replicate the behavior. It seems to be that the wiring issue is right there or at the handlebar which I highly doubt but will check again (from a known good bike but I suppose you never know). Now I need to figure it out.

A bench test on the solenoid found it lacking. It failed the basic alligator clip test on two batteries so a new one is in store. Think I might be that lucky?

Update: I purchased a used OEM solenoid from a breaker in NY and it seems to have done the trick. Installed new solenoid and I not only have lost the ceaseless cranking but I'm able to start the bike now. I'll install the new Shorai tonight (I was using a Wal-Mart AGM battery to test with) and take it for a spin to see if all is well. Al the connections checked out, no issues when I wiggle anything either. Good voltage everywhere.

With the new (to me) starter, I'm getting impressive torque when starting the bike, It spins quite well even with the starter clutch issue which I will need to address soon.