As has been posted in another thread, here's some relevant script content (from the September 26, 1966 Final Draft script for "Court Martial:"
From Scene 3:
INT. STONE'S OFFICE
FEATURING chart with legend:
STAR SHIP STATUS. Columns
lettered: Major Maintenance...Minor Maintenance...Ships
Incoming...Ships Cleared.
KIRK'S VOICE
[continuing his Captain's Log]
A full report of damages was
made to...
ANOTHER ANGLE - STONE
A NEGRO, whose bearing marks him as a man accustomed to
command. No longer a flight officer, his uniform is some-
what different from Kirk's, who is sitting opposite.
KIRK'S VOICE
...the Portmaster of Star Base
11: Senior Captain Stone.
STONE
I can't possibly have the
Enterprise ready that fast.
Kirk, who has been reading a document, looks up.
KIRK
This is
not a scheduled layover,
sir. I have a patrol course to
get back on.
(indicating chart)
Can they wait?
STONE
(considers, then)
If you exercise your
Mission-In-
Progress prerogative...they'll
have to.
KIRK
Consider it exercised.
Stone nods. He pushes button on desk.
STONE
Maintenance Section 18.
SOUND OF CLICK.
STONE
(a look at
the chart)
Your section is working on the
U.S.S.
Intrepid. Reschedule.
U.S.S.
Enterprise is on Priority One.
Stone clicks off the communicator. Nods at the paper Kirk
has been studying.
STONE
That makes three times you've
read it, Captain. Is there an
error?
(...and then the scene continues on as we know and love.)
So it looks like, generally, you make an appointment to get your starship fixed (or upgraded, I suppose) on a
scheduled layover--in which case it's probably first come, first served. But if you have an
unscheduled layover, then they'll try to squeeze you in if they can. But if you exercise your "
Mission-in-Progress" prerogative because you really need to get back to your patrol route and you just can't afford to be "fit in" to the schedule, then you are made a Priority One and get triaged to the front of the line.
It's pretty clear that, however it ends up looking to viewers and however folks might end up interpreting it, "Starbase M-11" was meant to be a
repair facility, not really a
construction facility (in the same sense as "I notice that they are doing some construction on the house across the street").
Construction can indeed sometimes mean
initial construction, but I think that's not the definition being used here; it's the
repair definition. As has been suggested, the notion that the
Enterprise was only 80% "completed" after being in service for decades seems wide of the mark.
It's pretty clear that Starbase 11 is a repair facility.
I don't think it was a starship construction facility either. But the wording from the episode is vague enough that one could claim that nothing contradicts it being a construction yard.