The ship in general has precious few windows, which makes their presence in the neck all the more curious.
Then again, we have seen that windows may be shuttered unless commanded to open, as in "Mark of Gideon". Perhaps the outer hull is filled with portholes, but most are kept closed almost 100% of the time - and the open holes in the neck actually stand proof to there being nobody there who'd care about an exterior view, which is why nobody bothers to close those things. (Clearly, Starfleet doesn't believe in darkening a starship for tactical reasons, as the bright navigation beacons continue to flash in all circumstances!)
The neck might be argued to be the part of the ship with the best view to the other
parts of the ship, which may be the overriding concern in window placement in starships of the era. But since the portholes we see do not bulge out at all, the view they offer is in fact quite poor...
Plotwise, we have some references to interior spaces on Deck 12 - a deck necessarily in the neck if we believe in the model where the saucer has 11 decks. Spock takes Mudd and his women there to meet Kirk in "Mudd's Women" (unless we decide he takes them there to be decontaminated and frisked before allowing them to enter the primary hull where Kirk waits, and the editing just skips this detour); the other Deck 12 references in Memory Alpha are arguable.
If we wriggle out of the "Mudd's Women" reference, we haven't seen the interior of the neck. But if we keep the reference, then after the turbolift ride to the supposed Deck 12, we see a space there that looks like Kirk's later quarters, with this corner
and this engineering-related alcove
and no sign of windows. A bit difficult to fit in there IMHO.
Let's not forget there's also a vertical turbolift shaft that passes through there and at least one long vertical Jeffries tube (with the 3-sided red ladder) or, several staggered Jeffries tube ladders.
We don't know if the shaft is vertical - an angled one would probably make more sense. Where does the evidence for a vertical ladderway (higher than two decks tall, anyway) come from?
The movie version of the ship appears to have a ladderway (or a stretch thereof) as seen when Spock climbs down to engineering to save the ship. It's also somewhat differently shaped. But while still featuring portholes, it also appears to feature an externally visible vertical element - a differently colored band of hull, perhaps marking the turboshaft. Or then that plasma conduit or warp core or whatever that goes up from engineering - but since the set also features a corridor extending forward from engineering, the intended Probert placement of that vertical shaft must be dismissed, which means the shaft won't be vertical all the way up but rather angled along the aft edge of the neck. That is, if it goes up at all, and doesn't truncate in some piece of machinery in the neck, say, a fuel tank like in TNG.
The TOS interior may have been identical to the TMP one, and possibly even functionally similar to the TNG one. Or then not.