SEOUL—President Donald Trump’s hawkish national security adviser, John Bolton, arrived here Tuesday with a daunting task: persuade South Korea’s dovish President Moon Jae-in not to abandon a vital intelligence-sharing agreement with Japan in his zeal for permanent peace with North Korea. The fear among U.S. and South Korean military people is that the Moon government, in a fit of spiraling anti-Japanese spite about other issues, might forget any semblance of cooperation. The sole beneficiary, they say, will be North Korea, whose propaganda machine has eagerly denounced the Japanese, called on Moon to hurry up with measures for a “peace regime” and attacked plans for small-scale computer-driven U.S.-Korean military exercises next month. As Bolton got off the plane at Osan Air Base, he tweeted that he was “looking forward to productive meetings with the leadership of our important ally.” But those honeyed words masked the urgency of what might seem mission impossible—salvaging what’s known as GSOMIA, the General Security of Information Agreement, signed in November 2016 after years of American prodding. The agreement is to be automatically renewed for another year on Aug. 24 unless one side or the other pulls out with 90 days’ notice—a deadline that’s long passed but…