Find your neutral switch on the motor that works the neutral light. Unplug the wire from it and ground it to the block with the key on. Make sure the block is clean where you ground it. If the light comes on, then you have a bad neutral switch. If this isn't the problem, then there may be a neutral relay bad or a bad wire somewhere. Check all of the wiring connections around your battery and fuses and starter solenoid.
First things first, with a quad of that age, have you checked all of the connections to see if they are solid and clean? also, have you checked for resistance on the battery cables?
OH, and welcome to the forum..