In neutral, the ball on the end of the switch is at the end of it's travel and the circuit (ground) which activates the neutral light is completed. When you select a gear, the ball is depressed breaking the circuit and turning off the light. Disconnect the wire from the switch - it's held by a single screw which is easily chewed up so make sure you use a proper fitting (preferably JIS) screwdriver. If the light stays on with the wire disconnected the problem is not the switch. In this case, you need to check the wiring as it is grounding elsewhere, or as in my case a few months back, you may have a corroded section. I fixed mine by cutting out the corroded part and splicing a new length of wire in. If you do need to remove the switch you shouldn't lose too much oil - give the bike a run first to ensure most of the oil is in the tank.
You're right in thinking this has been covered before. You will find numerous threads using the search function, including how to clean and overhaul the switch. Personally I would just replace a bad switch with a new or known good one though.
