Don't know if this is progress or not, but I've located that "missing / invisible" section 16. As you suggested, I inserted manual page breaks after sections 14 (appendix) and 15 (that section created only for the one-word title "Notes." Here's what I found:

Section 14, as expected / known, has all 3 headers throughout (first, even, and odd pages)

Section 15, as discovered (after inserting the 3 manual page breaks you suggested) has all 3 headers throughout (first, even, and odd pages).

Then for Section 16...
I go into "view headers / footers" (which identifies also the section, as does the status bar). After scrolling through the few pages I've manually created in section 15, seeing all the headers--first, even, and odd pages--suddenly I see "odd page header, section 16" without having seen "First page header, section 16." I continue scrolling through the entire section 16 (where all the endnotes appear, filling about 30 pages). The headings are, as usual, "even page header-Section 16; same as previous" and "Odd page header-Section 16." After all of that, and before the next section (17) I see "First Page Header-Section 16." No other section behaves that way, with the "first page header" appearing last.

I should add that the only way I can see this if I'm in the "view header / footer" mode. If I close that and put the cursor into the TEXT of the endnotes, I see displayed (in the status bar) the section of the manuscript to which the endnotes correspond (section 9, 10, 11, etc.) and NOT "section 16." I guess that is why I could not find the mysterious section 16 until now.

Is this some clue as to what is going on?

And I confess I have no clue what to do next. I've spent entire work days (weeks?) trying to solve this and am desperate (as you undoubtedly can sense).

Thank you, Charles, or anyone, for help.