A ground is a ground but which one of those grounds goes to the switch is important when you do your rewiring since you don't seem to be sure that the switch pins are in the middle of the connector and the illum pins are on the outside as per the FSM I have.
You seem to be adept at Redneck Engineering, so run a hot wire to one side of your test lamp (use a fuse) and a wire from one side of the switch (the uninstalled switch, not the wiring) to ground. Wire the other end of the test light to the other terminal on the switch. You should have a series circuit from hot to light to switch to ground. Push the button and the light should come on. This will verify the switch terminals and you should be able to tell which wire it is from that.
Just thought of this and don't want to edit all that above: You can use the light for the ground wire and run the hot straight to the switch.
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