Perhaps my whole approach is wrong from the start. 

Perhaps it's not a matter of paragraphs, chapters, etc; perhaps it's "a section of the book with a different purpose compared to the rest".

And that's how we have {bI'reS taymey} and {bertlham taymey}. Because the prologue has a specific purpose, which is different from the purpose of the main book/play, which in turn has a different purpose from the epilogue.

So perhaps a {taymey} is a part of a book/play/whatever, which could consist of one or more paragraphs/chapters, and with a purpose which is different than the purpose of the other taymey.