Imagine that you're watching, say, a human (a stand-in for said entity) from a distance, and, the second you physically see them with your own eyes - they do not necessarily have to see or hear you - they immediately know you're there until you break eye contact.
There are caveats to this:
If your eyes are pointed at it but you can't physically see it - for instance, there's a fogbank in the way, or the environment is too dark for you to see it, or you're blindfolded - this property will not take effect.
You have to make direct eye contact with a portion of its body in order for it to know you're there. This means that observation via camera or other such means doesn't trigger the effect.
You have to be able to perceive it in order for it to know you're there. The blind do not trigger this effect.
It still has normal senses - for the sake of the question, let's say it's essentially a human with this property "grafted on", with the full sensory suite that being a human entails.
This property works in vacuum.
When someone breaks eye contact, the effect ends, although the entity still remembers that someone was perceiving it. Think of it as hearing a jackhammer in the distance that suddenly stops - you stopped hearing it, but you still remember that you did hear it.
If said entity is completely covered in clothing, such that you can't see its body, this property does not take effect.
Whether or not observing it via mirrors causes it to know you're there is up to the question-answerer to decide, as is whether or not the entity knows the specific location or direction which it's being observed from.
The question: How, exactly, would such a thing be possible? To me, this seems like quantum mechanics insanity of the highest degree, and I have absolutely no idea how it would work, nor what tags I should put on this other than "senses".
I initially figured that giving this entity ultra-sensitive whiskers capable of detecting air current shifts would do the trick, or biological radar, but that didn't fit many of the criteria.