. . . If you look at TOS set plans, (which I don't have access to at the moment, but I'm sure someone can oblige)there was just enough room on the sound stage behind there to park the shuttle mockup, with the blue backdrop hiding the soundstage walls.
Here are the plans for the standing sets from TMOST
. I don't see enough room next to Engineering or anywhere else for the shuttlecraft. Maybe they used the adjacent soundstage?