There is rather scant evidence of two-shift sleep presented here; a single quote from some unknown writer and a single experiment with broadly interpreted results.
Not to mention that the "single quote" in the article is hardly from a "unknown" author (Charles Dickens), this BBC article on the same topic [0] has several other quotes from well known literature in the same period.
I don't know about books but this isn't the first time people have written about this. Doing a quick search on "between the sleeps" yields articles from early 2000s and 2010s.
And it’s one of those articles I read which had the tidbit about the books, and even some choice quotes. Not sure which article it was, but google should find it for you.
The article isn't a scientific enquiry, but it reports on the theme of the book At Day's Close: Night in Times Past (98 citations on Google Scholar)[1]. This book apparently packs a great amount of endnotes and sources.
[0] https://www.bbc.com/news/magazine-16964783.amp