The throne is mounted in the centre of a circular bathroom, it revolves on a precise swiss mechanism through which passes the necessary plumbing.
The time is marked on the wall and every hour is marked by a chime played on the bowl by a ball-cock valve, or spherical floatation device if you prefer.
The
Toilet could revolve either daily, hourly or every minute, the latter could be a bit quick. Other bathroom furniture could measure other increments. For example the sink could move around the circumference of the bathroom, though this could make getting in and out difficult if it occupied the same temporal space as the door.
Could bring new meaning to 'at the third stroke the time will be...'