I had always assumed that the Sunday closing an octave (and all non-outclassed feriae within it) would enjoy the same special “privileges” but I noticed on Low Sunday that the special Hanc igitur, Communicantes and sequence were not said, and I believe the sequence of Pentecost was dropped on its second Sunday as well. If octaves are supposed to extend a feast over eight days, why does the eighth not reflect this fully? What are the rules governing octaves and how they affect the days within them?
When the eighth day is Sunday, those special features give way to the Sunday. That is why the Christmas octave retains the Communicates on the first of January.