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The neutral safety switch is normally wired between your ignition switch and your starter solenoid to prevent the starter from engaging unless the transmission is in neutral. It's not absolutely needed but it's not a bad idea to use it or a clutch depress switch in your starter circuit.
My TKO500 came with a pigtail and a connector but like you, it only had one side of the connector. I just cut it off and replaced it with a waterproof 2-prong connector from a wiring supply house.
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Randy
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