32768's are a peeve of mine, and their history is illuminating.
The value was chosen (1970s?) for its obvious ease in converting to integral seconds, but it is difficult to get that value in the type of 'cut' that gets the best thermal stability ('A-T'), so a less-stable (and very small) one was used ('Tuning-Fork'). And hey! the thermal drift didn't even matter! if you have a reasonable-quality watch, look at the back. It's metal, isn't it? The front has an air-gap, and is therefore thermally-insulated. What is the temperature of the workings while the watch is securely strapped to your wrist? Pretty close to 37°, eh?
Now take that tried-and-true ol' reliable crystal and put it in a desk clock, and thermal drift might surprize you.
@DrFPGA If you pre-heated it to the right temp could you get it to switch every second?
Probably not. We're talking about something thermal that probably needs a large piece of hysteresis between the heating turn on and cooling to turn off. If you kept it heated up it would never turn off. You would need to use a higher voltage which might damage the tube or you could control an external heater to increase the rate of heating that shuts off when the relay goes on.
Reading Max's article again, it probably doesn't fit into his Vetinari Clock concept. It just the way my brain segways. I would use the relay to trigger the up/down counter on a 64 tap digital pot like the AD5113 and use a comparator to reset the pot when it hits 60. The comparator would trigger another digital pot that resets at 24 or 12. An all analog solution with no programming.
@Crusty...GREAT idea. You could have a curved line of RGB LEDs some distance above the sundial to simulate the sun, clear ones that have a narrow beam. and illuminate them one at a time, changing every 10 minutes or so (this implies 72 LEDs for 12 hours) and use one colour for day and another for night. Wouldn't need any motors, just some electronics to drive the LEDS. Since your LEDs would be fixed you wouldn't need to compensate for the seasons either...