I'll keep them close. Being at the dentist makes me nervous enough as it is, so it ends up being easier to just close my eyes so I don't have to see their tools and can instead visualize where they're working in my mouth.
open eyes. i tend to not look directly at them, but find a corner/something that i can look at in the room that's not their eyes and just look at that until they talk at some point
I keep my eyes closed. The main reason is that the light is too bright to keep them open. But even if it weren't, I would still feel awkward staring at the dentist.