When you stop at a traffic light and take your fott off of the clutch... the engine will switch off. Then when you step on the clutch... the engine will start back up. Not sure how it works with an automatic... but I suppose it switches off the engine when your still and your foot is on the brake pedal.
IF your car a Canadian spec car? Or maybe the previous owner used this euro switch to control something extra/aftermarket? Time to pull thet pannel off and follow any wires behind there!