Connor doesn't pry too deeply. He's content with the knowledge that V loves him back, that he trusts him. He won't dip into memories he doesn't need to, no matter how curious he may be, because if V wants him to know about it he'll tell him.

He can't stroke V's hair the way he wants to, so instead he offers up the suggestion, over the connection, that V sleep. Breaking the silence is the last thing he wants to do right now. He settles down into a position where he can go into standby mode after V has fallen asleep, keeping the connection active for now. Admittedly, he's curious as to what falling asleep feels like.