For all practical purposes the proximity switch behaves like a Normally Open mechanical switch.

Most people are overthinking the problem.

If your BoB input when unconnected is shows a light on the Mach3 diagnostics screen when it is configured, then the BoB has internal resistors to float the input 'High'. Putting a switch, relay or Normally open proximity switch (like wot you got!) between Ground and the BoB pin will push the input to Ground (Low) when operated and trigger the selected function.

The Black wire in the untriggered state has a high impedance and so it is possible to parallel them up to put all home switches to one input. I would use a routing diode on each output. If you are unsure I will breadboard a test and video it.

The Black wire will sink 300mA to ground. Any more than that, the switching transistor in the output stage of the device will make smoke signals that it has failed, and may even give you an audible indication (BANG!).