A simple indicator of the position of sequential thinking in a culture is its acceptance of the notion of consistency. The degree of inconsistency that we note in ancient documents should give us an idea of just how much emphasis that culture placed on reason.
One of the earliest documents to study here is Hammurabi's laws. These laws contain a number of obvious contradictions. There aren't many, but those few that exist are, to modern eyes, obvious. Moreover, because the laws address a great disparity of situations, there is little opportunity for contradiction. Only in overlapping situations could a contradiction arise -- and there are few overlapping situations recognized by those laws.
Another source lies closer to home: the Bible. Here we encounter a number of inconsistencies. For example, in Genesis, two versions of creation are offered. Genesis 1:1 through 1:31 offers the standard six days of creation, with man created on the last day. But then Genesis 2:4 through 2:7 offer a different version. In this second version, "no shrub of the field had yet appeared on the earth and no plant of the field had yet sprung up" when God made Adam out of the dust of the earth. In the first version, vegetation was created on the second day, and man on the sixth day, but in the latter version, man is created before vegetation. Unfortunately, the Bible has been pretty much scrubbed clean by editors over the last few thousand years. Over the years this poor document has undergone rearrangements, insertions, deletions, corrections, and all manner of other editorial improvements. Indeed, the example given above arose because a 7th century BC scholar apparently merged two drastically different versions of the Pentateuch. Therefore, we can't place much emphasis on the Bible.
The Egyptian Book of the Dead offers us another glimpse into ancient thinking, and it's not a pretty sight. It is clearly a religious tract, seething with spiritualism. As such, we must grant it some indulgence when combing it for logical inconsistencies. And in fact, I am unable to find such inconsistencies, not because the document is tightly reasoned, but rather because the whole thing is nonsensical. It is a collection of prayers to the gods, but the prayers meander about without any clear sense of purpose. Random jumbles of pious phrasings, not much more. Obviously, the people behind this document did not place much emphasis on making sense, much less being logical.
Looking to Greek civilization, we start with the two oldest documents in Greek literature: the Iliad and the Oddysey. Sure enough, a glaring inconsistency leaps out at us. Fairly early in the Iliad, Pylaimenes, king of the Paphlagonians, is killed. Much later, however, he shows up mourning the death of his son Harpalion. Modern moviegoers or novel-readers, confronted with such a glaring inconsistency, would howl with laughter; the Greeks don't seem to have noticed the problem.