Japan had partially mobilized the garrisons in Kyushu (Hiroshima and Kumamoto specifically) in preparation for if the Koreans did not agree to "to provide compensation for the incident," of course referring to the attack on the Un'yō in 1875. But by this point Japan had issues with actually going to war. War would have been extremely costly, and government expenses were already high elsewhere. A degree of instability was still in the archipelago, as you can imagine.
A full-scale invasion à la 1592 is extremely unlikely. Maybe a limited attack to further intimidate the Korean government into conceding (although this may have only limited effect on a continued Daewongun government), but there's no way in hell they're going for a repeat of 1592.