Latin divinare, from divinus (divine), possibly tied to deus (god), PIE *dyeu-, the bright sky. Rome industrialized it: augurs read birds, haruspices read livers, the Sibylline books read the state. Every technique assumed the same physics, the gods write, specialists read.
The skeptical anatomy: divination as apophenia with ceremony, the brain's pattern-hunger given official forms, entrails, cards, charts. It never dies because the appetite is the organ, not the technique.
*Dyeu-, the shining sky, built Zeus, deus, Jove, Jupiter, deity, Tuesday (Tiw's day), and possibly the first syllable of Diana. Divination is the reading department of a much larger institution: the entire sky-god vocabulary, the words that made heaven a text.
If the gods stopped answering, why did the question format survive?