Hmm do you just mean not pop/boy/girl band type of stuff?
Shiina Ringo was pretty popular back when I was listening to a lot of Japanese stuff. She can do a lot of styles but I remember her being punk rock jazzy. In the other direction, I was also into Pizzicato Five who are more retro 60s French vibes.
I lol'd. What does it say about our attention span though that you have to tell people to wait for it when it pretty much happens in 2 seconds