I just look out the window
And you are right. Timing based upon circling height means nothing if you lose sight of the runway. The problem is that many pilots design a pretty picture of a circling approach on their FMC MAP with various downwind, base and final approach waypoints and speeds. These are fed into the autopilot and flight director which means the pilot flies heads down without ever looking at the runway until turning final on autopilot watching the MAP and hoping to hell the runway appears in front out of the murk. This is accented in the simulator where all around vision is normally unavailable in the simulator design.
The circling manoeuvre is essentially visual flight. Of course you may have to scan the flight instruments on a dark no horizon night downwind and base but your eyes should also be scanning at the runway.