Bad neutral safety switch ???

If I turn the key to the start position, nothing happens, in any gear or park ('70 Duster 340, 727 trans) If the key is in the on position, I can jump the relay and it starts and runs ..

I put a voltage tester on the bottom yellow wire of the relay, and when my son turned the key, it lit up, so I'm guessing this rules out the ignition switch?

I took the wire next to it off (brown w/ yellow tracer) put a jumper on it and to a good ground and the car will start with the key, but in any gear.. Looked like that wire went down to the left side of the transmission and is part of a plug w/ 3 wires..I don't know what the other two wires are for.. I think this is the neutral safety switch ?? I removed the plug end, cleaned it up and all three terminals inside light up the voltage tester when turning the key to the start position...

I'd like to fix this the correct way and not by-pass the neutral safety switch... Can anyone help me here ???

Also, and this may or may not be related, but while removing an old tach on the steering column, a wire came loose near the fuse block, and I can't figure out what it's for.. It had a bare, stripped end and is dark green .. There's no voltage showing there, so I'm guessing it's a ground, but have no clue where it connected....

Really appreciate any help...

Thanks

Kenny