One of the terminals on your starter relay needs to be grounded for the relay to activate.
The switch you show (ouch) is just a ground switch.
It makes a ground for the solenoid to activate when the trans is in park or neutral.
One wire from the switch terminal to the starter relay does it.
Note where the pic says which connection is trans ground switch.
You can use a ring terminal on the switch with the appropriate nut, or if I remember correctly a temp sender terminal fits those as well.
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View attachment 1716258455