Yes, they would perceive meaning from patterns. The modern era attempted to jettison those kinds of concepts.Weren't people from the pre-modern era also extremely interested in the "heavenly bodies" and tracking their movements? And yeah this also includes believers from the most pious age when there was a united, catholic (small c) church that was providing European civilization with a Christian lens to view the world.
But practically speaking they could gain power from doing so. If the shaman or priests had the technical power to predict something like an eclipse it would be very convincing they have access to the gods.
And practically speaking we still aren't that removed from this seeing that people tend to worship "the science" and "scientists" again for their apparent technical prowess and predictive abilities.