Korean goverment has felt rushed to approach with Japanese government. Because korean economy is going to checkmate. Weak Chinese economy or conflict with Japan gives a big influence to not only selling off Korean stock and Korean won ,but also reducing production and income.
One of trigger which Korean economy has slackness is weak economy of China. Export business with China occupy approximately 10% of Korean GDP. Chinese economy has started to drop since 1st half, 2018 and it was accelerated by trade war with USA. It gives a negative impact to Korean stock price. And forex market also has started to sell off Korean won. Real GDP is maintained 2%. However real income is going to minus level.
Stock price is recovering little bit because trade war between China and USA is "pending" at this moment. However Chinese economy is still not good. Therefore Korea government wants to solve a conflict with Japan for domestic economy in Korea.
Hoewver Japanese government has to have a firm attitude. Any conpromise are not needed at this timing.