Neutral light WORKS PERFECTLY but.with.or.without.key.on!?!?!??!

Been owning riding and fixing bikes for 55 years - never had this happen before! Please do NOT suggest that the neutral (transmission-grounding) switch has failed. That would make it not work as it should, or work all the time that the key is on. Please do NOT say it's a blown fuse (they aren't and it isn't a lack of electricity it's electricity when and where it has no right to be).

Endless searching on this and other forums turns up lots of people for whom the neutral light is always on if the key is on (which means the ground wire and/or neutral switch are shorted to ground obviously). Also plenty of people never see the happy green light (no power getting to it or the ground side isn't doing what it should obviously). It's an LED so it can ONLY work if the voltage is passing through it in the correct direction, from positive side to ground and the ground side is just fine. So where is it getting that 12v from when the key is turned off and removed?

Again the neutral light goes on in neutral and off in every gear, doesn't flicker and behaves normally except that I have to park the bike in gear to stop it draining the battery overnight, it's driving me crazy and since I bought the bike in pieces I don't know whether this has always been the case or something I've done recently (like replacing the engine) has made this happen somehow. All I know is that it's getting power from the10A fuse 5th from the top of the fuse block (front left side of tank) because when I pull it out the light does go to sleep. All other electrics work perfectly without issue and the bike (now) starts and runs beautifully.

I carefully took apart the instrument cluster and cleaned all the dead bugs, ant eggs and spider webs out of it, sprayed electrical cleaner everywhere and put it back together with no change. The neutral light seems to sit on top of an IC and can't be got at so perhaps there's an electricity leak right on that board and I'll have to change the whole dash cluster - but that's a bit overkill and will give the bike an unbelievable zero kms... I did find that the ONLY live wire (key off) in that multiplug is the brown one 3rd from the top right so if that's NOT supposed to be live (key off) then it suggests a short between two wires deep within the wiring harness. Now I've seen many things diagnosed as a short in the main harness over the years - but never seen anything that actually turned out to be deep within the harness unless there's clear physical evidence of trauma to explain it. Removing the clutch safety switch makes no difference so if you've got an early Ninja 650 and care to compare yours with what I've described maybe you can tell me what's different.

In an ideal world someone will say "Yes that happened to me just do so-and-so and it'll be fixed" but I doubt I'll be that lucky. Any sensible suggestions?