So here’s the interesting thing about where McCoy stands (and I admit, I seized on the “right-hand man” pun without fully thinking about McCoy’s usual stance).
McCoy stands on Kirk’s left side, and the left side of the captain’s chair, most of the time.
But there are some exceptions.
Most of them have something to do with a disruption to the natural order of things (Kirk in the middle, McCoy to his left, Spock to his right). The first kind of disruption is when Kirk isn’t captain at the moment.
When Bones is fighting with the idea of Spock as leader (the middle of The Tholian Web, The Galileo Seven) he tends to stand on his left. It seems to be a visual representation of McCoy refusing to relinquish his traditional spot on Jim’s left side, and thus refusing to accept a change in leadership.
When McCoy is supporting Spock as temporary captain while Jim is in peril (The Doomsday Machine, the end of The Tholian Web, Arena), he stands on Spock’s right side.
The clearest example of this is in Arena, where he starts in his normal spot and moves over when he fully registers what’s happened; he literally invites Spock into the chair, and then moves to Spock’s normal spot.
At the end of The Tholian Web, he’s still to Kirk’s left, but to Spock’s right.
The second type of disruption occurs when Spock is in danger. When Spock is out of the picture, or when McCoy is extremely worried for Spock, he tends to stand on Jim’s right, where Spock should be. This happens both on the Bridge (Operation: Annihilate!)
and elsewhere (A Private Little War).
This also happens when Spock is taken over by an alien entity, such as Kollos (Is There in Truth No Beauty?) You can see McCoy saving Spock’s rightful spot here.
When Spock has been taken over by Henoch (Return to Tomorrow) and is in the captain’s chair, McCoy is desperately trying to save his life: again, standing at his right side.
The best representation of the “Spock in Peril Switch,” though, is in The Immunity Syndrome. After Spock leaves the ship, McCoy stands at Jim’s right - both by the Captain’s chair and everywhere else.
It’s like he’s keeping Spock’s spot warm; he always has hope that Spock will return, and speaks to this perhaps more directly in this episode than any other (until, of course, his speech to Spock’s comatose body in The Search For Spock). “Spock. Is it me, Jim? Am I so sentimental that I just have to keep believing that he’s still alive in that mass of protoplasm?” Even Spock makes a joke that McCoy is out of order, calling him “Captain McCoy.”
But as soon as they find out Spock’s alive and they’re pulling him to safety? Watch McCoy move.
So, yes, upon more thought, that seems to be what Bones is doing here. He’s keeping hope (and Spock) alive, standing in his place, and keeping it safe for him.
And I still have Feelings about it.