Re: wiring diagram needed
That diagram is for a Mercruiser. He has an OMC 800.
It is indeed a mechanical shift diagram...just the wrong one.
Did the 800 OMC have a shift interrupt circuit?
It won't be your neutral switch, that just disables your starter.
If you have a safety lanyard("man-overboard") switch, that could be your problem. Those are an inline switch in your ignition circuit.
Another thing could be your ignition switch itself. Next time you are out running your boat, wiggle the key slightly to see if you get the same problem.
If all of that doesn't work, may have to trace all the wiring too make sure all connections are good. Since it sounds like you did a repower, it is possible the person who did the swap messed up on a connector or splice possibly.