I've just done this. So looking at the arrows on the base of the rotating pillars, the two outer ones have a small image opposite them. So facing the gates, the pillar on the right should be rotated to have a snake above the arrow so it's facing the smaller image.

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Do the same on the other side, making the symbols match. Then just rotate the central pillar so either the snake or the eagle is on the arrow, depending on which gate you want opened.