In MMJoy2Setup I don't know. You can map two logical buttons ("joystick") for ON and OFF of physical ON-OFF-ON switch (H/W button), but don't see option for map two physical (H/W button) button (of ON-OFF-ON switch) for the same logical button ("joystick" #3).

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But using an keymapper (SVmapper, JoyToKey...) "mapped on press" and "mapped on release" functions is possible.

Or use a DPDT ON-ON-ON switch.

https://www.mouser.com/Electromechanical/Switches/Toggle-Switches/_/N-5g2j?P=1z0z2xkZ1z0z2o3