1995 King Quad 250? won't start.. no clicks or cranks - has green neutral light

[hunky]

This old boy has been coastal so lots of rust. But when I turn the key, nothing. Green neutral light works, head/tail lights work. Was running fine when I parked it for a few months.. no issues with starter. This did happen once before (last year).. not sure what overcame it.. maybe playing around with gear shifter.. but not sure if that was what did it. But doesn't seem to do anything now when I play around with it while hitting the start button.

I did take apart the handlebar mounted start button housing and looked it over. Couldn't figure anything out there, but looked the same as when I had the problem last year. Put my probes on various wires there but didn't learn anything.. not sure how it is wired.

So this first image there is a connector with 2 wires coming from forward (the male part of connector) - one blue and one blue w/ red stripe. The blue continues down to a post near where the gear shifter enters the housing. (Second image). I was wondering about that.. I opened up the connector and the 2 wires (coming from forward) show continuity when I put my probes on 'em. Thought that was weird, but maybe supposed to be like that? I turned on the key and tested for voltage but didn't find any.

I'm just unaware of how to test for anything. Would be interesting to put 12 volts to the starter, but not sure about doing that or how. The wires going in are kind of hard to get to. I suppose I could take out the starter.. but wanted to ask if there is something easier to check first.

Thanks for looking!