Here is a link to the wiring diagrams in the Tech Section.
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1294779818When the neutral light (and starter circuit) go out.....does everything else still work (lights, turns signals, horn, etc)?
The indicator lights in the speedometer are spliced into the wires for the turn signals and high beam - so you could completely unhook the speedometer indicator light harness and the bike would still function normally - However it could be the Neutral light is required for the stater circuit to work.....as it is connected to the diode in the starter circuit and may have to be in the circuit for the starter to work (I am not certain of this). In order to check this connector you will have to get the tank up off the frame....this requires removing the seat, unhooking petcock vacuum and fuel lines - the stock vacuum petcock also hits the frame and will need to be removed on most bikes.....then you can unbolt the back of the tank and slide it back out of the front mounts and tip the front of the gas tank up to reach the connector (you will not have to unhook the speedometer cable unless you remove the tank).
The other harness connectors you should check are on the left and right side of the frame....you may be able to reach them without removing the fuel tank. They are at the front of the tank very near to the bottom.