Arthur gives out his notice responsibly before disappearing: he lets everyone know he'll be out of contact for at least a month, and won't even be accepting calls for emergencies. He's taking personal time, and will not be bothered, and that includes Eames.
(Eames doesn't care about that. He shadows Arthur, and Arthur knows it.)
Arthur used to be named Aidan, and his brother is missing-presumed-dead. Brendan-became-Bryce-became-Neal-went-back-to-being-Bryce and fucking died, and Arthur wants to know why. He needs to know why.
And Chuck, that silly little boy Bryce fell in love with and Neal couldn't forget, was there. He was there when Brendan died, and Arthur will learn everything he knows, no matter what it takes.
Brendan wouldn't want Chuck to come to harm, but Brendan's fucking dead, so he gets no say at all.
Chuck's a spy, like Bryce. He's also a geek, and a dork, and so nice it burns. Arthur's not used to nice. (Also, he can hear Eames laughing.)
Chuck's earnest, and after he stares at Arthur for a long, awkward moment (and the gun Arthur's holding), he slumps down, and he says, "I am so sorry," and the damnedest thing is, Arthur believes him.
So, Chuck is actually a spy with a computer in his head (Bryce's fault) and he knows far too many things about Arthur for Arthur to be comfortable with. But he won't use the information against Arthur, because (for some insane reason) he thinks Arthur's a good guy. (Eames is laughing again.)
"He talked about you, sometimes," Chuck tells him. "He missed you."
Arthur says nothing, but his hand is not on his gun.
When Chuck's keepers come to his rescue (Arthur is not impressed, and Eames makes half a dozen snarky remarks before they've even cleared LA), Arthur is long gone.
He doesn't have his brother's body, but he knows exactly how and why Brendan died.
Chuck is still alive, because it would've have made Brendan's death worthless if he wasn't.
Arthur finishes out his month of vacation in New York. Burke is completely different from Chuck, but Arthur likes him a bit more, and Eames has fun finding and replacing his favorite pieces at the Met.
Finally, as the month draws to a close, Eames pulls Arthur into his arms and asks softly, "Will you tell me about him?"
Aidan and Brendan are both dead. But Arthur almost sees them, young and fierce and strong, as he tells Eames things no one has ever heard before.
(Casey is annoyed, and Sarah furious, but Chuck never does explain what happened in those four hours he was off-grid.
He's alive. Because he knew Bryce so well, he knows what that means.)