I recall reading articles about this issue some years ago, and after reading of a new development - March 25, I added that and another nine or ten more from a quick search. An unexpected and interesting surpise was finding an article about the persecution of Jehovah's Witnesses during Japan's occupation of Korea last century. I'll add some more articles later, but I think this is a decent start:
May 13, 2015: A Life Sentence from Birth: Story of a South Korean Conscientious Objector (https://www.amnesty.org/en/latest/campaigns/2015/05/a-life-sentence-from-birth-story-of-a-south-korean-conscientious-objector/) (Amnesty International)
Oct. 3, 2015: South Korean Jehovah's Witnesses Face Stigma of Not Serving in Army (https://web.archive.org/web/20160317155230/https://www.nytimes.com/2015/10/04/world/south-korean-jehovahs-witnesses-face-stigma-of-not-serving-in-army.html)(The New York Times/The Internet Archive)
Dec. 19, 2016: Is South Korea Thawing to Conscientious Objection? (https://www.koreaherald.com/article/1182308) (The Korea Herald)
March 7, 2019: All Witnesses Imprisoned for Conscientious Objection in South Korea Now Free (https://www.jw.org/en/news/region/south-korea/All-Witnesses-Imprisoned-for-Conscientious-Objection-in-South-Korea-Now-Free/) (Jehovah's Witnesses)
Nov. 11, 2018: S. Korea Eases Rules on Military Service (https://global.chinadaily.com.cn/a/201811/02/WS5bdbbc25a310eff30328626c.html) (China Daily)
July 9, 2020: South Korea's Conscientious Objectors Are Getting an Alternative to Military Service (https://thediplomat.com/2020/07/south-koreas-conscientious-objectors-are-getting-an-alternative-to-military-service/) (The Diplomat)
Oct. 19. 2019: Korea's Jehovah's Witnesses Saw Deep Hardship - Under Japanese Occupation (https://english.hani.co.kr/arti/english_edition/e_national/206230.html) (Hankyoreh)
Oct. 27, 2020: South Korean Jehovah's Witnesses Start Prison Work Terms (https://www.bbc.com/news/world-asia-54694964) (BBC)
Sept 2, 2022: Inside South Korea's Harsh Alternative to Military Service (https://time.com/6208211/south-korea-military-service-draft-conscription-conscientious-objector/) (Time Magazine)
March 26, 2023: Top Court Finds Jehovah's Witness Guilty of Evading Civilian Service (https://www.koreaherald.com/article/3090723) (the Korean Herald)
March 25, 2026: Choosing Jail Over Enlistment. One Korean Man's Pacifist Stand (https://www.koreaherald.com/article/10700466) (The Korea Herald)