Sounds electrical if all above is true:)
check the year of electrical parts for the THROTTLE.OVER. RIDE. SYSTEM.
88-02 had 4 wire stators 03-06 had 5 wire stators.
88-02 you just unplug the brain under front nose
03-06 you need to splice wires.
could be your stator/flywheel magnets/ timing key...