I think you should be searching about "RFID" technology. There are even some Arduino sensors that imitate this behavior and are frequently used for automated door locks controlled by Arduinos. I'm not really up on the technology, but I think it all works on magnetic induction. The fob usually has a coil of wire that is used to (I think) both power the fob circuitry and communicate with the other sensor. Some googling on "RFID" might prove better info than my answer.
They are probably similar to these microwave Doppler detectors, or this one.Very cheap and remarkably sensitive! They will respond to a human moving anywhere in a 5m x 5m or larger room.
What you are looking for is a capacitive sensor for the arduino. If the cars body is metal you just connect that sensor to your cars body and when you get near the car it will give the arduino higher readings