I am referring to both men's and women's uniforms, as both the gakuran and sailor-fuku seem to be derived from military (specifically naval) uniforms, particularly if you include the hat, which has now seemed to have largely fallen out of fashion.
I would be interested to know why hats have fallen out of fashion, now that I think about it, as well as other questions of fashion, such as why the color seems to be universally about the same, why the patterns are generally flat, what kinds of schools use these, etc.
But mostly, I want to know how this very Western-looking outfit came to be associated with Japan and Korea so intimately.
Sailor fuku were in fact derived from Western military uniforms. At the time of the Meiji Restoration, where Japan began rapidly modernizing, one thing that was quickly established was mandatory public education. At the time, most of the foreigners in Japan at the time were advisers of a military persuasion, especially naval. The dress was quite fascinating to the Japanese (mostly because it was different from their traditional garb) and it also happened to be easy to make. Japan adopted many Western customs, as can be seen here with a picture of the Emperor Meiji wearing a European-style uniform. This was no exception. Sailor suits were a popular dress for European children at the time (for instance, here's a portrait of Edward VII in one) so it is likely that Japan adopted a similar garb for their own children in schools.
In the 1900s, Japan annexed Korea in a series of treaties and after fighting a few wars for dominion (including the 1st Sino-Japanese and Russo-Japanese wars). One of the things that they quickly implemented was a mandatory education system, both to cultivate an educated worker base (as the typical Korean peasant at the time was illiterate) as well as to teach/brainwash (depending on who you are talking to) the Koreans as to why Japan should rule their country. While the classes primarily taught the Korean language (and the alphabet, Hangul) and a pro-Japan view of Korean history, they incorporated many Japanese ideas, including the sailor uniforms.
I unfortunately cannot comment on fashion trends in this regard. Hopefully somebody can provide more details here?
You should be careful with how you word this question. It sounds like you're saying all Korean and Japanese school uniforms are this style. I can't speak to the Japanese part of the question but this is definitely not true in Korea. Maybe half of the schools in my city in Korea wear that "sailor" style uniforms but the other half don't.
