Curious, at which point is it defined that the One Power carries knowledge? If that were the case then the moment one accessed the power would they not just KNOW how to channel, and not just instinctual stuff like rand "Willing" things to happen - but the knowledge of weaves? If that is the case why are any weaves or talents lost? Why would anything need to be rediscovered? Just distill a venerable Aes Sedai's knowledge into the Wheel of Time version of a Pensieve and call it a day - boom...everyone be making Ter'Angreal in no time.
Additionally and related in some ways, few other channelers seem to have the same experience as Rand and LTT, which could be explained to the power in the SOUL that he is rebirthed from and not the power itself. He was unique in being GIVEN knowledge rather than having to be taught it in a traditional sense.
This is supported in some ways with Hawkwing: "I have fought by your side times beyond number, Lews Therin, and faced you as many more. The Wheel spins us out for its purposes, not ours, to serve the Pattern. I know you, if you do not know yourself. We will drive these invaders out for you."
So either he too had a similar experience with past knowledge as Rand, or his soul - once freed from its mortal coil - knows all the knowledge of his past. Either way it seems this knowledge is soulbound rather than power driven. Mat being able to bring forth memories from his blood implies as such as well.
So I am not of a mind that the Eye of the World in any way contained any knowledge of the One Power, Channeling, or any such things but was exactly as it was stated. A repository of untainted Saidin. To be used in a way that even those that created it could not comprehend. I do not believe they in any way intended for it to be used in the way Rand used it so any "knowledge" imparted to him if it even was possible would not have jived with his use. That is like someone writing a manual in Aramaic about technical support for a HP printer, and you are using the manual to diagnose problems with your dishwasher and only understand English.