Lord Vetinari turned away, took some papers from a desk drawer, walked to a wall, touched a certain area and stepped quickly through the hidden door that noiselessly swung open.
Beyond was a corridor, lit by borrowed light from high windows and paved with small flagstones. He walked forward, said "...no, this is Tuesday..." and moved his descending foot so that it landed on a stone that in every respect appeared to be exactly the same as its fellows.
Anyone overhearing his progress along the passages and stairs may have caught muttered phrases on the lines of "...the moon is...waning..." and "yes, it is before noon." A really keen listener would have heard the faint whirring and ticking inside the walls.
A really keen and paranoid listener would have reflected that anything the Lord Vetinari said aloud even when he was alone might not be totally worth believing. Not, certainly, if your life depended on it.