"I'd argue the "Dagger of the Mind" transporter is a separate entity not only by design, but also by virtue of being somewhere down in the engineering hull. After all, the only partially insane van Gelder seems to be making his way up from that facility towards the bridge, with Deck 14 along the route. Plus, this is a rare all-cargo transport operation, so possibly associated with a special room connected to cargo or supply holds. (Perhaps personnel transporters have the starscape for purely aesthetic reasons, covering a circuit board identical to this one, while cargo has no sense of aesthetics?)"
I concur but the engineering deck plans I'm currently finalizing suggest the cargo transporter not to be lower than Deck 14 (one deck lower we're running out of space). I'd say it's the same one as the one in "The Enemy Within" ("gathering specimen") were the engineering panel was added within the year before "Dagger of the Mind".
I've done an extensive study of the Season One transporters and the star chart seems to be somewhat inconclusive:
The Cage & Where No Man Has Gone Before:
cluster star chart between door and transporter platform, galaxy chart next to transporter console.
Corbomite Maneuver & Mudd's Women:
cluster star chart next to transporter console, no lines whatsoever on it
The Enemy Within & The Man Trap & The Naked Time:
cluster star chart, one
horizontal white line, one
vertical black line
Starting with "Charlie X" all transporter rooms have the cluster star chart with two
white lines and the black one
The transporter room in "Charlie X" is close to a turbolift (same with "This Side of Paradise" in the scene with the crew queue).
The one in "Dagger of the Mind" has the unique engineering panel in the back.
The (other) transporter room in "Tomorrow is Yesterday" and "This Side of Paradise" (Spock and Kirk fighting) has the yellow wall food / landing party gear dispenser but not
the star chart.
My whole point is that each transporter room has to have unique features allowing distinction of a crew member just having beamed back on board ("Which transporter room am I in?").
On deck 14 I have the cargo transporter at the port side bow while the other one with the turbolift ("Charlie X", "This Side of Paradise" and suggested by movement in "Tomorrow Is Yesterday" and "Doomsday Machine" is at the starboard side stern.
The one from "Where No Man Has Gone Before" is at the port side bow on Deck 10 (suggested by "The Changeling" as they're trying to get Nomad ASAP to the nearest transporter room without using a turbolift close by!). I think this is also the one (now slightly changed) from "The Naked Time" as it has this unique decontamination feature. Since there is engineering personnel active on Deck 10 wearing radiation protection suits (WNM) I'd lke to think that at the end of their duty shifts they use this transporter for decontamination of their gear.
"I'm not sure if I want to believe in the symmetrical arrangement of four saucer rooms postulated by FJ, but at least a rotationally symmetrical arrangement of two saucer rooms (with the starboard room aft of the transverse corridor, the port one forward of it) would seem to be supported. And in any case, the idea of "the transporter room" indicating the existence of just one would seem to be insupportable..."
I believe we are looking at a minimum
of four transporters as suggested by the producers in The Making of Star Trek
and TAS. Of course these should be dispersed over the ship as otherwise you'd have longer queues than just the one seen in "This Side of Paradise".