dawm:
It is a momentary switch. When held down it supplies ground to its output wire.
That suggests that the input wire is normally at 12v (but car voltages can rise to 15v) so you would need a voltage divider to bring that down to a max of 5v for the Arduino.
Then the Arduino could easily detect and time the button press.
I presume you will be controlling the extra lights with some 12v automotive relays and an Arduino cannot control them directly. You can use the Arduino to operate a transistor which controls the current in the relay's coil circuit.
...R