Arduino and car's 12V switch
The situation may be a little more complex than you imagine.
Since your switch (potentiometer) is an input device to the car ECU to set intent, you would need to disconnect the signal wire from the ECU so you can read the switch position. Then you need to generate a voltage into the ECU to provide control from the Arduino.   

It's highly likely that the switch is NOT on a regulated power supply, so the voltage may vary from say 10 V (starting) through almost 15 V (charging). This will be coped with by the ECU (it knows what the battery voltage is). There may also be fault sensing to discern if the switch has failed, so the current sourced  or sunk from the ECU may be important. 

You can deal with the high input voltage with a simple resistive divider, though it's worth having overvoltage protection.  

Perhaps something like this:







simulate this circuit &ndash; Schematic created using CircuitLab