Well, I built the first version of a complete clock using the Geiger counter, an interface shield, an Arduino Uno and a Lavet motor clock display. The Arduino sketch uses detected clicks from the Geiger counter to figure out updated guesses estimates of how many Arduno micros() there are in a standard second and uses that to drive the clock display. The idea is to calibrate the speed of the Arduino's not-too-accurate ceramic resonator clock using the count of the decays detected by the Geiger counter.

While I'm pretty happy with the way it works, continued observation of the click rate from the Geiger counter worries me. The click rate continues to decline slowly with time. At the beginning of the week it was just under 51 clicks per second, now it's just under 48.  Since I don't want to build the equivalent of  "pig airport" -- a bunch of fancy, complicated infrastructure based on the fundamentally flawed idea that pigs can fly -- I need to figure out why the click rate is not constant.

As [Thomas] observed, there are several critical aspects of the way the Geiger counter detector is built that could be the cause of what I see. I've tried to make sure the radioactive source itself is stable and in a stable relationship with the GM tube. So, I'll look first at things I haven't tried to control. For example, perhaps the voltage on the GM tube is wandering around. Or maybe changes like this are just what one sees if a Geiger counter is run continuously for a week. For that I'll need to do some research.