Hey, I never noticed that before....

[Maurice]

The shot a similar scene looking at the viewer with Chekov, IIRC.

 

[Just a Bill]

Yeah, I believe there's a bit of a three-quarters rear view—from the right side of and behind the captain's chair—that they used a lot, and I think that has Hadley/Blackburn at navigation.

Yup, that's it!

After reading your reply, it occurred to me that I could hit Memory Alpha > Hadley > Appearances and look for episodes marked "stock footage." There are three. In the first, Metamorphosis, I couldn't find Billy unless it's just his shoulder in one of the Sulu scenes (a shoulder that might be wearing a second-pilot uniform). However, the other two episodes did deliver, and in spades: they gave me a brand-new Hey, I never noticed that before!

The Cloud Minders and Turnabout Intruder both deliver the three-quarter view of Hadley's head, but in two slightly different scenes. The first features Spock; the second, Kirk. The surprise for me is that the two setups are otherwise nearly identical. Same camera position & angle, same lack of dialog, same blocking of the conn officer starting in the chair, looking at the viewscreen, then standing up out of the chair. The kicker is that they both feature the same four other actors in the same exact seats: Jeannie Malone, Ron Veto, George Takei, and Billy Blackburn. Billy's two poses are virtually identical, to the point that even his shadows look the same.

The Cloud Minders (left); Turnabout Intruder (right)​

I gotta believe they filmed both of these sequences specifically for use as stock shots, on the same day. "Thanks Bill; okay Leonard, your turn." If the camera was tied down well, maybe they were even able to use the same viewscreen matte for both.

One final stupid observation: The Turnabout scene is a double cheat: not only is Chekov being faked, so is Janice Lester!