The Invisible Clock Tower took eight years and twenty-three million dollars to build, and is constantly teleporting. Despite having no fixed location and being impossible to observe, Cecil describes it in "The Drawbridge" as a "lovely structure that keeps impeccable time."
Cecil mentions in "The Phone Call" that Carlos has asked him if anyone has ever actually seen the clock tower. Cecil sees nothing unusual about the tower's invisibility or its translocation, so he ascribes Carlos' questions to his not understanding basic architecture.
In "A Blinking Light up on the Mountain", the watchman that lives in the clock tower rings its bell to warn residents about the impending danger approaching the town from the empty desert.