We don’t know for sure whether the priestly courses rotated perpetually or reset at the civic New Year. We do know that each course/family drew lots at least twice a year, and all 'families' drew during major festivals. The good news is that we don’t need to know which family was due to draw at the civic new year. In this approach, we simply view *any* 24 to 26 week period as offering Zechariah one, two or three chances to serve. Of course, that still begs the question – where to begin?
I have suggested elsewhere that God did not send Gabriel to Jerusalem until after the sabbatical year ended in September of 9 BC. That’s a theological assumption, but it’s hard to start any earlier than about that time, anyway. From that starting point, then, the Tabernacles Festival and Day of Atonement were Abijah-lot-drawing chances one and two. If Gabriel did not come at those times, the 24 week cycle of courses would revolve once again between September and March. In all, the odds are strongest that Gabriel came sooner rather than later - perhaps early November (if the cycle reset each autumn), or we might take December as the median of statistical likelihood (if the cycle was perpetual, and thus undeterminable).
Again, however, this is just an example. None of this helps us date Jesus' birth with any precision. Given certain parameters, however, a range of dates can be constructed that fits what we do know. Here is the key challenge.
To be continued...