It would take a bit of work to accomplish without spoiling the surprise by calling Dean and asking him where he was. First looking for the car, then flitting around from place to place in a potentially expanding search pattern to find him.

Gabriel eventually takes off for another part of the apartment because laying around doing nothing all night is a good way to result in a bored archangel. Not helpful for the world in general. Better that he sees if there's any late night programming actually worth bothering with.