EOS-1N focus points disappear when rotated

I’m having a very strange problem with my new-to-me 1N. Sometimes when I select focus points, they will light only partially, or for the outer two, not at all. However, if I turn the camera body 90° and then back, they all light up solid and stay so. This happens regularly, although I cannot reliably trigger it, and the turn-to-fix behavior is consistent.

I’m at a loss. This behavior is independent of eye position or glasses. If I hadn’t seen it happen repeatedly, I would tell me I was making things up, but it’s definitely happening.