I take whatever you have to offer, but here are some things I like in films of that kind that I probably would like in a book too:
-An 1900 to 1960(?) setting.
-The teachers being involved (as victims, suspect, whatever)
-the idea of that school (headmistress, board,…) being the evil (like a narrative of the story that doesn’t have to be right)
-light on the students relationships (the story can be character driven. I am fine with long period of time where no murder or missing person or something happens)
-A non paranomal explanation (if your suggestion is paranomal please note that if that book doesn’t make that clear in the text at the back)
And here is my favourite film from that genre, so if you have seen it you could know the vibe I like: ‘the house that screamed’
by _A__P_
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Plain Bad Heroines by Emily Danforth I think actually fits all of your criteria – one to check out!