[Anaraxes]

Is this a place where their society naturally evolved? If so, would they even have a concept of regular time being important? You can collect taxes whenever you need them. For that matter, you could count "days" and collect taxes every 100 days, whether that's the same amount of time or not. (What's the distribution of the variable lengths of time? It will have an average, and over a long enough period of time, might well be predictable enough.) Are the people human enough to want to eat or sleep regularly (or at least fairly so)? Your enlistment might be for life, mustering out when you're disabled either through injury or simply old age, whether that's infirmity or whenever the hair on your temples or sideburns turn grey. Or life events, like the birth of your first grandchild.

Or are they transplants from some other society that did have regular time already, and are trying to preserve that part of their society?

How technological are they? Water clocks, hourglasses, pendulum clocks, spring clocks, quartz crystals, atomic clocks, pulsars... (But the first question is more important. You don't invent clocks until after you've decided you need to keep more accurate track of time.)

Lots of background questions come up with this kind of worldbuilding.