@TIN_MAN - sure, here's a list of all the times "engineering section" was said in dialogue in chronological order.
I only mention TDOTD because although the crew's memories and perceptions are messed with, we as the viewer supposedly are not affected and we see the entity leave the "engineering section" and exit the secondary hull. This places at least one "engineering section" in the secondary hull. "The Apple" has
multiple engineering sections. "The Ultimate Computer" has an interesting bit where the Exeter's engineering section was hit and damaged their impulse engines. That could mean the engineering section refers to impulse engines or it could mean that both systems are counted as part of the section and Spock saw that the impulse portion got hit. In "The Omega Glory" I believe they showed multiple engineering room sets (one with Kirk's party and one empty).
4 Mudds Women: SULU: Captain Kirk,
engineering section reports our entire life-support system is now on batteries.
24 Space Seed: SPOCK [OC]: Captain, acknowledge. Unable to flood
Engineering section. I suspect
24 Space Seed: SCOTT [OC]: This is Scott. Captain's headed for the
Engineering section. I'll follow in case
38 The Apple: SCOTT [OC]: I'll have
all engineering sections working on the circuits immediately. Transporter'll be ready in an hour.
39 Mirror Mirror: SPOCK: Explain computer activity in the
engineering section.
41 I Mudd: KIRK: Scotty? Security, the intruder is in the
engineering section. Have all units converge on that point.
44 Journey to Babel: KIRK: This is the
engineering section. There are a number of emergency back-up systems for the main controls. Over here are a number of control computers.
53 The Ultimate Computer: WESLEY: You've been chosen to test the M-5, Jim. There'll be a series of routine research and contact problems for the M-5 to solve,plus navigational maneuvers and the war games problem. If the M-5 works under actual conditions as well as it has under simulated tests,it will mean a revolution in space technology as great as warp drive. When your crew has been removed, the ship's
engineering section will be modified to contain the computer.
53 The Ultimate Computer: SPOCK: Hit in
engineering section. Possible damage to her impulse engines. She's still maneuverable on warp drive.
54 The Omega Glory: SPOCK: We're locked onto the Exeter's
engineering section, Captain.
54 The Omega Glory: KIRK: This is Captain Kirk of the USS Enterprise. Is anyone on board? If there is, and you can hear me, please respond by intercom to the
engineering section.
57 Elaan of Troyius: SPOCK [OC]: Spock here, Captain. I am triangulating now. It's coming from the
engineering section.
66 The Day of The Dove: KANG [OC]: I have captured your
engineering section. I now control this ship's power and life-support systems.
66 The Day of The Dove: SPOCK: Alien detected in the
engineering section, near reactor number three.