Please add Jumong (2006-07). The gay relationship is overt, albeit a very side story.One of the 1st sageuk I watched, still one of my favorites, 81 episodes long, the gay relationship was so openly and adorably and frankly shown.
https://www.tparents.org/Library/Unification/Talks/Mickler/Mickler-100115.htm "Jumong's relatively liberal approach toward romantic attachments is most apparent in the series' depiction of a homosexual liaison between the merchant Yuntabal's chief strategist Sayong and Jumong's lieutenant Hyupbo. Though subject to a good deal of comic relief and joking, at least early-on, their relationship is finally not only tolerated but openly acknowledged. Here, as elsewhere, Jumong reflects tensions in contemporary Korean sexual mores."
https://www.journals.uts.edu/volume-x-2009/94-i-jumong-i-a-window-into-korean-and-unification-culture "...the series' depiction of a homosexual relationship between the merchant Yuntabal's chief strategist Sayong and Jumong's lieutenant Hyupbo. Though subject to a good deal of comic relief and joking early on, their liaison is finally not only tolerated but openly acknowledged. Here Jumong may or may not be at odds with popular Korean culture, but certainly it is so with the Unification movement. The Unification position on homosexuality, though sympathetic to persons, is unyielding in its opposition to homosexual practices."
https://www.koreatimes.co.kr/www/common/printpreview.asp?categoryCode=229&newsIdx=12906
"These days, it is the mass media that bring the so-called ``homos'' much closer to the public. Box office mega hit ``The King and Clown,'' ``Road Movie,'' ``No Regret 2006,'' and small screen hit ``Coffee Prince'' and ``Jumong'' portrayed some aspects of gays in Korea. They had trouble with their identities at first, but accepted it and paved their own way through it. "