One can make some measurements to determine the performances of the clock -- both to estimate the randomness as well as to evaluate the long-term accuracy. 

The distribution of intervals between individual ticks shows a very different picture between a normal clock and our contraption.

Left: tick duration you want from a normal clock. Right: tick duration you get from Lord Vetinari's clock

The tick duration in our clock has the expected exponential distribution of time intervals, with short ticks being balanced out by long ones. The mean value of this distribution is very close to 1, providing the long-term accuracy of the timepiece.

Looking at the duration (in seconds) of an hour measured by our clock we are again greeted with a fair bit of randomness.

Left: Time series of the duration of an hour, as measured by Lord Vetinari's clock. Right: Histogram of the same values

While the duration of each individual hour, as counted by our clock, can be off by more than a minute, the histogram shows that the standard deviation is about 60 seconds. That is to be expected from counting statistics, with sigma being on the order of the square root of our measured counts -- here about 3600.