An access control mechanism such as a movable barrier operator (70) has a first time window unit (72) that is responsive to one or more triggers (71) (such as a delayed-closure button). An event detector (73) then monitors for one or more events of interest during a corresponding first time window. For example, the event detector can monitor for evidence that a vehicle is moving towards a garage exit or has effected an exit from the garage. A second time window unit (74) responsive at least to the event detector and optionally as well to the first time window unit then responds with a second time window. Upon conclusion of the second time window, a movable barrier closer (75) initiates movement of the corresponding movable barrier towards a closed position (or other position of interest).