Mukai is best known for his 2 failures at world level. One of those saw him suffering an opening round technical draw with Pongsaklek Wonjongkam in a bout for the WBC Flyweight title, that fight lasted just 47 seconds. Unfortunately for Mukai his second world title tilt was a brutal beating at the hands of Srisaket Sor Rungvisai in 2013 as Srisaket recorded his only successful defense of the WBC Super Flyweight title. Although he has suffered those set backs he is a beautifully talented boxer with great movement and heart though unfortunately has a lack of power which will likely prevent him from ever winning a world title.
As for Tomiyama he has come up short in just a single world title fight, back in 2009 when he was stopped in 8 by Nobuo Nashiro, having given the then WBA Super Flyweight champion a real scare. Despite his loss to Tomiyama he is actually better known for his much more recent battle with Genesis Servania which ended with Tomiyama losing a technical decision in Macau. Sadly for those who remember Tomiyama's loss to Servania he's not looked good since struggling over domestic journeyman Kanae Onogi and being stopped in 3 rounds by a rampaging Kentaro Masuda.
Whilst this isn't a world title eliminator or a title bout...it is a very important bout for both men and the loser is likely looking at the end of their career whilst the winner may find themselves in a Japanese title fight by the end of the year. With that said it's clear that this is a major cross roads bout and huge credit needs to be given to both men for agreeing to it.