"A School Story"
from Ghost Stories of an Antiquary, Part 2, by M. R. James
Oooh, creepy.
Somewhat predictable? No tidy explanation? Well, yes, but still. Old-fashioned creepiness abounds.
I found the summaries of the "typical ghost stories told at a school" plenty creepy, too.
Thank you again, Barbara Michaels, for bringing M. R. James to my attention.