Author here. Even though its proximity puts it pretty far above background, the marbles are still a fairly weak source, so from the "electronics logic longevity" side it's not something I've really thought about. But the Geiger-Muller tube does have a finite (though very large) number of events it can record, so I cut the voltage to it when the device is in "clock mode" and not functioning as an RNG.
Doesn't answer your question, but might be a start.