Are there actually cram school positions for high school students?

There does not seem to be any cram school positions for high school students.

Perhaps it is because they go to adult cram schools to get ready for IELTS etc.

I’ve wondered this as well.
Certainly I would assume there is but I’ve never seen it. Maybe there is less focus on English in senior high and if they go to buxi they work on other subjects. Or as you said, maybe they just go to adult cram schools if they go at all.

There are some, mostly private cram schools that run high school students’ classes and even some university/college students. They seem to focus on either GEPT/TOEIC/IELTS/TOEFL. I’ve taught some of them, and you just have to look around or find a connection who can arrange you to meet with the schools.