The Ancients would by this part of the month be negotiating final arrangements for the Big Celebration. And I imagine those who are chosen to lead parades get a little nervous at the prospect of something going wrong, and as a result probably become edgy and bad tempered and a nightmare to be around. There'd be outfits and headdresses to worry about, words to remember and a host of concerns, all of which in my view accrue to any celebration devoted to precision. A solstice is a single moment, so short in duration it requires a discipline best left to mathematics, or a clock, to comprehend. And especially scary when that single moment becomes important to meaning. An error could be disaster.
Sometimes it would rain, or a morning fog, or some other spoiler or pillaging heathen would blanket the sky. The wise would point and say "that's where the sun should be." And there would be a general acceptance that most likely the sun was where it should be, and most likely winter was coming in the same why that it always had done, before the Priests took charge so they might reap the rewards as well as the dangers of responsibility. Then one midsummer, the weather crystal clear, a slight chill from the east, the crowd wishful in the early light, and the priest and his political allies in their tall hats and pomp, high up on the wooden dais, each of them thinking, "Yes, I did this." I have to think some of them dumb enough to believed it, and tomorrow I'll tell you why those on the dais still like to sacrifice the pure.