Getting your DNA tested and uploading the data to GEDmatch.com were both great ideas for trying to find your half-brother. According to https://www.nytimes.com/2016/08/28/world/asia/south-korea-adoptees-325kamra.html, there is a nonprofit organization called 325 Kamra whose web site is https://www.325kamra.org/. They say their mission is "to reunite Korean families separated by war, adoption, death and tragedy by DNA testing Korean adoptees, armed services personnel who served in Korea, and anyone of Korean descent to expand the worldwide database." Their FAQ page https://www.325kamra.org/faq mentions "if you are a Korean vet or a family member of a Korean vet you also can qualify for a free DNA kit".
You've already paid for your DNA test, so you don't need a free kit from them, but it sounds like they might be willing to help you if you contact them at the email address they list at https://www.325kamra.org/faq.
Now let's talk a bit about the DNA analysis. The only people whose DNA matches are relevant to finding your half-brother are (1) the DNA of your half-brother himself, (2) the DNA of your half-brother's children (your half-nieces/half-nephews) if any; and (3) the DNA of your half-brother's grandchildren (your half great-nieces/half great-nephews). I suppose there's a tiny chance that your half-brother could have great-grandchildren who have had DNA tests done, but since the Korean war started in 1950, making your half-brother at most 68 years old, it seems unlikely.
If you look at https://dnapainter.com/tools/sharedcmv3, you'll see that half-siblings nearly all share between 1317 and 2312 cM of DNA, with an average of 1783 cM. Half-niece/nephews share 500–1446 cM (average 891), and half great-nieces/half great-nephews share 125-765 cM (average 432).
All of that means if your half-brother or one of his children or even one of his grandchildren is on GEDmatch, they will very likely be your top match, aside from some close relatives who are presumably already known to you. As the other answer from Cyn notes, there is some small chance that the person with 119 cM could be the grandchild of your half-brother, but it seems small.
As Cyn notes, it's possible that the haplogroups listed for some people on GEDmatch could be useful. The one it labels "Mt" means mitochondrial DNA haplogroup, which is passed from mother to child; your half-brother would be expected to have an Mt haplogroup that occurs among Korean people. The one it labels "Y" is the Y chromosome, passed from father to son; your half-brother would be expected to have a Y haplogroup which occurs among people of your father's ancestry. If you have a brother who would do a DNA test, then your brother and half-brother would be expected to have the same Y haplogroup; the same would be true of a male first cousin of yours born to your father's brother, if any such people exist.
I have not done a search like yours, so I would be happy to defer to someone with greater knowledge, but my expectation is that any match for your half-brother or one of his descendants will be extremely obvious, right at the top of your one-to-many list on GEDmatch; or else the person/people you're looking for will not appear at all, because they do not have results on GEDmatch.