2.1.293 Part 1 Section 17.10.1, evenAndOddHeaders (Different Even/Odd Page Headers and Footers)

a.   The standard says the determination of even and odd pages is based on the ordinality of the pages.

Word uses the starting value of page numbering for the parent section to determine if the first page is even or odd.  This is specified with the start attribute on pgNUmType element.

b.   The standard says a missing header type shall use a new blank header.

If a header is missing in a section beyond the first section, Word uses the header from the previous section.