[utopia]

Righto .. I have some neutral switch info for you.

I have the same switch on my yr2000 M750 and I have had a similar problem .. for the last 2 or 3 yrs in fact, but I've lived with it until now.
Neutral light glows in any gear, although to be fair it does glow a little more brightly in neutral.
I had heard that sometimes this can cured by fitting a slightly thicker shim/sealing washer beneath the switch but in my case the switch fails no matter how far you screw it out of its housing. Maybe this is worth trying in your case but don't get your hopes up.
I've just been to Ducati Coventry and bought a new switch and sadly I have to report that the price is a very salty £50 odd including the vat. Ouch.
The wire is soldered to the switch. It doesn't unplug at that point.
The hex is 13mm.
The black seal around the wire where it joins the switch will pass a 13mm ring spanner but its very tight and has to be persuaded. I haven't tried a box spanner yet but it looks like that would be even tighter and my guess is that it might not pass. I could check this later.
In any case, a box spanner will not pass over the Tyco Superseal connector on the other end unless you first remove the terminal from its housing. There are instructions online showing how this is done but you would need to improvise some sort of tool to pull out the red "anti-backout device" and then poke around with a needle or somesuch to release the plastic tab which retains the terminal in the housing.
I took a different approach and cut a slot in an old ring spanner to allow it to pass over the wire. I dunno whether this will work though as there isn't much room to turn it before the spanner will foul on the recessed housing.

That's about it for now, except to report that I temporarily cured my switch recently by removing it and soaking it in engine oil. It worked fine for about 400 miles (bizarre but true) but then it returned to its former, failed state.
I include this for interest value only.

I will report back with any further info gleaned from the refitting process.
That may take a day or two though ... I need to modify the wiring on mine as I have a homemade gizmo attached which enables the engine to start/run when the sidestand is down, as long as the bike is in neutral.

ps. part number for the switch is 53940201A