Case 580SE Neutral Switch Grounding

I own a 580SE that had a previous engine overhaul and new transmission. There's a few issues I need to resolve but the machine feels basically "solid". Here's the latest issue; This winter it was starting fine when suddenly I could not get it to crank when turning the key. I could easily get it to start by jumping it at the starter so I have been starting it each time that way. I've now decided I need to get the problem identified and fixed. I've searched and read messages relating to this problem. I found the Neutral Switch and disconnected the harness. I placed a jumper wire on the wire harness and nothing changed. I was disappointed and surprised. So this morning at 4:00, I could stand it no more and got up to check a couple of things. I placed a 12 volt test light on the machine. I clipped the ground wire to the ground stud on the starter. I was going to check and see if I had power in the wiring harness when I turned the key. WITH THE KEY TURNED OFF, I was surprised to have full power to one of the wires in this harness. Turning the key to START changed nothing. I then switched the test light to the other wire in this same harness. There was no power with the key to off position. When I turned the key to start, the engine cranked and started. I was surprised as the test light never did light with it in this position. I turned the key off and repeated the sequence several times. Each time I had the same result. When the test light was present, it completed a ground circuit to that harness and everything works fine. When I returned the harness to the Neutral Switch, It quit working again. I do have power to the gauges and I can barely hear a clinking sound in the dash area when I try to start it. I'm not sure what to do next. I could just ground that wire and things would start fine but it would override the Neutral Switch. For safely reasons, I don't want to do that. What do you suggest? I didn't think that harness would have any ground function in it. I was also surprised to have full power in that same harness (other wire of the pair) when the key was in the Off position. What do you think? I appreciate the great advice and knowledge of those on this Board.

Case 580SE Neutral Switch Grounding