A couple more things:
In Rand's flashbacks of the Aiel's history in Rhuidean (specifically the 7th vision I believe), he see's from Jonai's perspective and enters on Aes Sedai discussing another person's visions and have Callandor and Lews Therin's banner at hand along with Someshta the Nyhm (aka The Green Man). They make mention of the taint on Saidin and a handful of young male Aes Sedai that they could get help from as it wouldn't be strong in them yet. So we know this is post sealing and the banner has yet to be hidden (thus lending to the fact that the pool was not already in place to hide the seal and/or the banner at that time).
We can also infer that the seals were hidden during and/or post breaking as in one of the earlier books it makes the comment about the Amyrlin Seat being titled "Watcher of the Seals", but that they no longer know where the Seals are located as the knowledge was lost around the time of the Trolloc Wars.
It's also unlikely that Rand using the power in the Eye caused the weakening of the seals as at this point it's clear they are ALREADY weakening considering at least Ishamael, Aginor and Balthamel had freed themselves from Shayol Ghul before the power there is used.
As far as the purpose of the Eye goes, it likely was involved in the Prophecies of the Dragon in some fashion and the Eye needed to be emptied to gain access to the Dragon banner which in turn was needed to direct the forces that were called by the Horn of Valere. Both Callandor and the banner were present when those ancient Aes Sedai were (presumably) discussing the visions of the Dragon being reborn (with the Green Man present no less) so they clearly must have been planning the securing/hiding of said items.
It perhaps even was placed in case of the need to 'kick start' the reborn Dragon into being made aware of his ability to use Saidin, or even to help bring Lews Therin and/or his memories near the surface. It's clear that some stuff was placed specifically for him (such as Callandor) and this could very easily be yet another such thing.