I reblogged a post with a dumb joke involving Kronos whispering in Percy's head during SoN for the bit, but then it got me thinking:
Imagine when Luke dies, he's the linchpin of Kronos stitching himself back together and reverts to being a bunch of chopped up bits. Most of him goes back to Tartarus but one little fragment attaches to Percy because he's Right There, and so powerful that a sliver of Kronos can go undetected.
And the sliver wasn't gonna do anything, just watch the rest of Percy's life 'cause that could give him useful intelligence when he tries to come back again in a couple thousand years, or at least entertaining. Besides, all it has the strength to do is talk, and it's not like Percy would listen to him.
But then Hera wipes his memory.
And look, Kronos wouldn't be able to try to come back in ten of Percy's lifetimes even if Percy was fully trying to help him. So Kronos isn't gonna try and get Percy to work for him, per se. But he can help Percy out while he's amnesiastic, establish some trust before Percy remembers why he distrusts him.
I don't entirely know where this is going. Percy does his breaker-of-cycles thing and gets Kronos to not be such a dick? Dark Percy with time powers? Percy telling everything in Tartarus "fuck off or else" with the Titan King's voice? All of the above? Idk.