James T. Kirk was capable of many things, and was responsible for great Federation victories, but he wasn't made to deal with political and diplomatic affairs; his rank as admiral couldn't change it and Spock's presence at his side was the only thing that kept him from dying of boredom during a meeting that had already lasted way too long.
The bond between them was formed years ago, but Kirk still caught himself marveled by the sensation of constant touch between their minds; the simple fact that Vulcans could form bonds with non-telepathic beings was already amazing, but to know he was never truly alone and, regardless of the distance between them, Spock would always be able to sense at least his deepest feelings caused in him a sense of safety without which he no longer knew how to live; and it was through the bond that Spock could sense that Kirk was about to fall asleep and, to keep him from causing a diplomatic incident, he offered the first two fingers of his left hand without a word, knowing his intent would be clear trough the bond.
With his face as blank as Spock's, and also keeping his right has at the table by his pad, Kirk reciprocated the gesture, that to him as a human meant nothing, but that he learned to cherish and even long for, as much because he knew what it meant to his lover as for the response he could fell through the bond, and when Spock relieved the control over his own mind, Kirk's mind was invaded with so much fondness, love and affection that he couldn't help but smile.