"I'll try." He is tired. He's aware of how much sleep he needs, too, to recover from a weeklong mission.

And he does try. He gets four hours, and he wakes peacefully from a dream where he and K are sitting and watching a blank television. K is dead, most of the skin peeling off his face, exposing his molars, tearing at the corners of his lips when he speaks.

It means when he wakes he spends a very long time just studying K, watching him breathing.