Ok, I know the board you are using it's not just a simple breakout board it's actually a combined 100khz motion controller and breakout board. You have movement so the mach3 plugin must be working so won't get into that.

The switches are simple lever types so no special requirements really. Simply connect one wire to Gnd and the other to the input.
Port 3 is correct and so are the pins 1 to 4, (turn off emulated) Now because the limits on pin 3 work then I would first try switching the homes to this input and see if anything changes. If not it could be a plug-in issue.?
To confirm you could switch the Limits to pin 4, if they work then you know the input is good and the problem is elsewhere, if not then it could be a blown input.

Now I know with other external motion controllers that the homing duties are usually taken away from mach3 and the plug-in handles them so it could be this that is causing the issue.? So first thing to do is reinstall the plug-in. Or it could be that the plug-in doesn't support homing or works differently from the norm.?

Other than that I can't help other than to say throw it in the bin and buy a decent motion controller, these Chinese things are rubbish and USB isn't reliable, so together they don't make a great controller.