The neutral light comes on when the switch is grounded,so I suspect that the wire to the switch is pinched and creating a ground. The most common place for this to happen is between the countershaft sprocket cover and the crankcase.I would start by removing that cover and taking a look there. while you are in there you can check the switch, it is below the sprocket and slightly toward the front. Remove the wire,it just pushes onto the switch ,connect an ohm meter to the switch connector and the other end to a ground such as the crankcase. The switch should show an open circuit when you shift the bike into gear and closed in neutral. I suspect you will find a pinched wire not a faulty switch.
The same thing happened on my 81 CB750K and the cause was a frayed wire that was making contact with the frame. We ran a new wires right through and with some heat shrink, the problem has never come back. Very rarely does the switch give any trouble