I discovered that, after breaking the clock, you can attempt to fix it with a Lore:Mystical + Intelligence check!
This is the clue I got afterwards:
A glowing, viscous fluid flows up from the ground to the top of a chamber inside the device. Sifting through the synth shards, you find pieces ofa filigreed grating - diamonds within diamonds. It has been shattered into several pieces by your blow, making the remnants hard to find. Fixtures around the sides of the chamber suggest that the grating was attached in the midst of the fluid, perhaps as some sort of sieve.
The grating is too shattered to fix, but perhaps you could find a replacement.
A circinate symbol is etched inside of the chamber like a maker's mark. You commit it to memory.
This could open up a whole lot of great options! We would be able to turn the day to night, free the Nychthemeron, and then fix the clock, which would still allow us to convince the Cultists that we're the Changing God without using Tidal Surge!
How do we replace the grating? I spoke to the Master Foreman, Prata, Aligern, Callistege and the scientists in the Order of Truth. It wasn't a dialogue option. I don't remember finding any gratings on my travels.