Returning to the issue of the pylon for a moment, is there anything to say that those (or indeed any of the) round and rectangular "windows" seen on the ship have to actually be windows
Throughout the three years of TOS we only ever saw 3 confirmed windows - two in Conscience of the King
(which were square) and one in Mark of Gideon
(which was more rectangular, but still different from the ones on the Enterprise model).
Additionally, MOG showed us that portholes have both interior and exterior shutters (this feature nicely deals with the discreprencies in interior and exterior window shapes)
So, could some or indeed all of the "windows" seen on the flyby shots each week have in fact been sensors or something? It would certainly explain why there are so many of them in the engineering hull! I mean, shouldn't those engineers be working instead of stargazing?
It's enough to compare the TOS Enterprise with the Galaxy class starship a hundred years later; we see the Galaxy has a vast and extensive lateral sensor array on the rim of the saucer AND the engineering hull, in addition to a ring of sensors on the dorsal and ventral side of the saucer. The TOS vessel has only those glowing domes on the saucer and one on the back of the secondary hull; those would seem to be inadequate for a ship on a mission of exploration IMO.
The dark "windows" probably contain optics/telescope elements intended to image distant objects across the electromagnetic spectrum, from radio wave through X-ray and everything in between. The lit windows are probably active scanners, some type of radars/lidars, spectrometers, and a few might even contain ordinary searchlights.
I might even go so far as to guess that the observation lounge from "Mark of Gideon" might have been a sensor bay that was intentionally left empty so it could function as an observation port. The sensor elements of the Enterprise would all be housed in those sensor bays so they could be serviced by engineers in a shirtsleeve environment.
They could be similarly 'transparent to radiation' the same way the domes were labeled - you can put different sensor devices behind them, maybe they're on a turntable so 5 or 10 devices could all be aimed out of a single unit one at a time.
Or, hey, maybe some are widows. Maybe some are sensors...
Actually, I think that ALL of them are windows, but I'm suggesting here that they're not necessarily windows meant for people to be looking out into space. They were probably installed in the first place so scientific instruments could be placed on the inside of the hull where they could be maintained and serviced on a regular basis and still have a view of space outside the ship.
IOW, in the TOS ship, the windows probably act as sensor viewports and various scanning devices are installed behind them. It would certainly explain why we so rarely see those windows from the inside of the ship: the only places you're likely to find them are empty sensor bays where your view of the window will be obstructed by equipment anyway.