The wheels in Shinji's head are definitely chugging now, and when he puts the pieces of what Kai's implying together, his eyes light up in understanding. Ah, so that's the angle he's going for.

He gives Kyoko a sidelong glance, and while he does want to take her promise at face value, he can't deny.... having her right there would make it much easier to make sure she does let herself rest. He doesn't feel right pushing her too hard about it, but if he doesn't make too big a fuss, maybe she'll be more okay with the idea...?

"I mean, if it'll make it easier for you, Kai."

Think of his condition! It will ease his worries! This is not a bad idea, awkward as it may be.