I have not read the Discworld series, but this sounds insidious as Hell!!! I love it.
I asked Google Gemini for book sources, got this: "The Vetinari Clock originates from Sir Terry Pratchett's Discworld series of books, specifically appearing in the waiting room of Lord Vetinari, a recurring character. It is first described in Feet of Clay and also features in Going Postal, where its purpose is to psychologically unsettle visitors by ticking irregularly while still maintaining accurate time"