SEOUL – South Korea’s liberal government next month faces its most crucial test since the Candlelight Revolution that between 2016 and 2017 resulted in the ouster and jailing of the president’s conservative predecessor, Park Geun-hye.

Under South Korea’s “democracy constitution” dating from the 1987 mass protest against another dictatorial regime, the current president, Moon Jae-in, can’t run for a second five-year term. He would dearly like to see the candidate of his ruling Democratic Party of Korea, Lee Jae-myung, defeat the conservative candidate of the People Power Party, Yoon Suk-yeol, in the election for president on March 9. 

Mr. Lee, like Mr. Moon an impassioned advocate of reconciliation with North Korea, would press for dialogue with Kim Jong-un, who has spurned North-South meetings since the failure of his second summit with President Trump in Hanoi three years ago.

After having been a clear favorite in polling, Mr. Lee has slipped behind while battling reports of scandals stemming from his time as a provincial governor and as mayor of a city near the capital. He faces an ongoing investigation into real estate funding from which his enemies say he’s financed his campaign.

Mr. Yoon served for two years as the government’s top prosecutor in Mr. Moon’s leftist administration, but quit amid criticism for going after the president’s justice minister, a liberal who was forced to resign. Now he’s infuriated his former boss by saying he would, if elected, investigate corruption under Mr. Moon and press claims from when Mr. Lee was mayor of Seongnam, south of Seoul. Two people implicated in real estate dealings there have committed suicide rather than face trials in which they might have spilled secrets.

Mr. Yoon has also aroused the ire of liberals by saying he hopes to “rebuild” close ties with America and insist on North Korea giving up its nuclear program. Mr. Kim, in addition to ordering seven missile tests this year, is believed to be on the verge of testing a long-range ballistic missile capable of carrying a warhead to America and may even order the North’s seventh nuclear test. North Korea last tested a nuke in September 2017 and an ICBM two months later.

Mr. Yoon has said he would jettison Mr. Moon’s calls for a declaration with North Korea and China formally ending the Korean War — which concluded in a truce, not a peace treaty, in July 1953 — and he would like to see American and South Korean troops resume joint military exercises on the ground, at sea, and in the air. The U.S. still has 28,500 troops in Korea, but American commanders say joint exercises now conducted largely on computers are far from adequate. Mr. Trump called off the war games after his first summit with Mr. Kim in Singapore, in June 2018. 

Surprisingly, however, Kim Jong-un’s rhetoric and North Korea’s missile tests are of secondary interest among voters. People tell me they’re mostly concerned by reports of corruption and economic difficulties marked by youth unemployment, a widening rich-poor gap, and rising prices. Mr. Lee’s wife has had to apologize for treating his aides like servants and for misusing government vehicles, and Mr. Yoon’s wife apologized for making up credentials to gain a post at a university, but denied a report that she once worked as a hostess in a nightclub.

Mr. Yoon has been criticized by conservatives in his own party for having brought the case against Mr. Moon’s predecessor, Park Geun-hye, daughter of the late dictator Park Chung-hee, who was given a lengthy prison sentence. In a bid to show his compassion and win support for Mr. Lee, Mr. Moon has exonerated her. Mr. Yoon, wishing her well, said he was “just doing my job” by prosecuting her. He could soon be taking on a much bigger job.