It's funny those abandoned apartments have more visitors now than they did back in the days of yore when they were occupied. I keep seeing all manners of shady Glitches down there tending secret herb gardens and sneaking through the shadowy hidden passages.
The trick is to stand far enough away that you can still click the button with the mouse (without getting moved closer). Then you should have enough time to dash to the left before the gate closes again.
:(