Looks like this wire is there for when the switch is in the run position. The spring is for when you turn to the start position, and it pushes the switch back and holds it in the run position rather than remaining in the start position so that the starter stays engaged.
I am not aware of a way to get the spring by itself as it normally comes with a replacement switch.
You may be able to get one from a salvage yard but more than likely they will be included in the replacement switch.
Please see the wiring diagram below which shows this wire.
Thanks
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Sunday, April 10th, 2022 AT 11:34 AM