The other thing to check it the connection to the neutral switch. If I understand what you posted, when the electric starter does not work, the neutral light is not working either. There is a plug low down on the right side of the motor with two wires, one for the neutral light, and one for the reverse light. Check the plug to make sure that it is secure.
ATCnut
82 185s - sold
83 200x (hopped up)
84 200x (stock)
84 70 (lost this one to the DMV)
85 70 (soon to have lights, a foot brake, and CDI ignition)
84 200es (parts trike) - sold
85 350X (the best)
85 350X (siezed motor, dream of a poweroll kit someday)
85 250sx (frame was trash, got parted out)
86 250sx (the tractor)
86 250sx (a nicer tractor)
86 250sx (an even nicer tractor)
87 200x (parts trike, its really rough, a dog was chewing on it for a while)
87 250es Big Red (the tank!!)