The feeling of having a pair of eyes on you is aways terrifying, especially when you're unable to find the source of where it's coming from. But what about multiple pairs of eyes? That feeling only increases ten fold, and the paranoia would probably start to set in. It would mean that there was more than one person, right? One person can't have multiple eyes, it wasn't possible. So it would only mean that it had to be multiple people having their eyes on you, right? ..Right?

..but what about a demon?

It was definitely plausible. However, if it was a demon behind this feeling of being watched, why hasn't it attacked yet? Demons prey on humans to eat, not follow around in the shadows just to follow you around.