Due to the life he’s lived so far, Khan isn’t comfortable sleeping while there’s people around (unless it’s his crew, someone he trusts and whom he knows won’t harm him in his sleep or let anyone else harm him).
Kirk realizes that. They’ve known each other for a while so he’s well aware.
Which is why Kirk is so surprised when, one time when it’s just the two of them in a shuttle, after Khan hasn’t slept for days, the augment just dozes off sitting next to Kirk.
After gaping for a while, Kirk realizes just how much that means Khan trusts him and his integrity.