Well, if you want some random guesses, the element eggs and the verses both point to an order...its explained bt Bricot in Gridania...and, while we can't trade eggs in certain order, we do can speak with NPCs in this order.

Note that they're exactly the weather that happens at 3 nations (Jihli verses also say something about weathers)...Ul'dah has sandstorm (earth), Limsa has rain (water) and Gridania has thunderstorm (lightning)...here what bricot says:

Bricot: Once we have all the eggs, Jihli'll ready the summoning. Oh, and I'll help! I remember exactly what she told me! The Archon egg goes in the, um, middle, and the others go around it. Lightning, then water, then earth...or was it water, then lightning, then earth...or...um...

Also, we can see that these 3 elements are related....so lightning is supposed to be in the middle since, no matter the orderit is the middle (earth > lightning > water or water < lightning < earth) so it could indicate an order of talking.

But, anyway, its just completely random guesses...but i'd love to see the event having an update triggered sunday (since the new caps are already ingame i don't think a patch would be needed...just like events have timer to end they might have timer to start too if needed).