The Station Square rank is staffed all night (sample). After midnight, cars line up on the station side of the square, under the lights and the camera.
Between midnight and 06:00 every zone fare costs $4 more (Example prices). The fare is the same at the rank and by phone, so there is no need to wait outside if it is cold: call and the car comes to the door.
Working a late shift every week? Ask the office about a standing booking; the same driver can collect you at the same time each night.