I do feel the issue to be a little more complicated (but definitely favor the skylight interpretation).
In my post # 664 here
I illustrated the differences of the upper side of the saucer hull (11' VFX model) between Pike's Enterprise
from "The Cage" and Kirk's Enterprise
in "Where No Man Has Gone Before" (unfortunately the VFX footage of the revised upper side didn't make it into the episode but we - now - know what was there!).
It think it's safe to assume that the EVA platforms (like in TMP) would have been these rectangular, yellow patches (which the 11' VFX model kept at least near the impulse engines' cover hatches).
The Pike Enterprise
had no illuminated rectangular windows and lacked the four upper side white / illuminated rectangles.
The moment the windows were illuminated those four rectangles were added. Considering that these windows apparently generate some "milk glass" effect (i.e. you can't see what's behind them but you probably can look out through these), I'd assume the same would apply for the skylights.
According to the TMP novelization the new rec room seen in the film on the starboard stern of the saucer used to be the sports area on the TOS Enterprise
and probably included the gym from "Charlie X".
The gym, however, is a rectangular room that would look odd in the room arrangement of the saucer hull. To assume the white rectangle to be a skylight not only corresponds with the nearby location of the gym but would also justify to have a rectangular room at this location.