I need a 3-way switch, ON, OFF, AUTO.
Most three way switches have three connections, the center connected to the lower, the center connected to the upper and the center connector not connected to anything.
This is not directly compatible with any digital system. It is best to have the center connected to an analogue input, with a 10K resistor also connected from the input to +5V. Then the one end of the switch are connected to a 10K resistor to ground and the other switch connector to a 4K7 resistor to ground.
Do an analogue read and look at the result, that will give you three different readings.