I have some personal experience over the years with this, and recently my Guides suggested that this was a very important topic to explore.
Not only have I seen many instances of people reacting to being stared at when they had their backs (women especially), when no sensory clues could be normally identified... as I'm sure all of us have.
In recent years I have been wondering about why people walking in this typically sparse European crowd, or in stores/shops or public transport seem to bump into me or touch me inadvertently harshly in contrast to local norms. (It might be OK in some exotic cultures I've read but it is not the norm here). Usually they apologize with a few words or a gesture. And I do not mean drunks, very old or impaired people, some of whom will have a lowered sense of their environment.
Another thing was that when in walking I tried to overtake someone, I would mostly feel that I was far less perceivable at times than other people. True, I have a supersensitive sense of hearing - I usually sleep with earplugs - verified by doctors' examinations when I wsa drafted to the Army here already. It runs in the family.
Then one day I tried something which I have tried at the threshold of consciousness many times earlier - e.g. when trying to move very quickly in a crowd at the Metro (Budapest underground), but never believed in it. While walking quickly among commuters getting off the train here, I tried to concentrate on people - oncomers or when I tried to pass someone much slower. (I am a quick walker and have very long legs.) I simply got tired of being swept to the absolute edge on a daily basis. Sometimes they would react to my dog on a leash before noticing me. (As a recent biker, I try to softly ring the bell to warn people every time because walkers hate being suddenly biked on...)
The thought I held at a nonverbal level was merely that I would go on in a certain direction - watch out! And after that, there could be still quick nonverbal balances worked out and variables for age, being affected by alcohol or in a heated argument or whatever. Plus there are born bullies who would sometimes bump int you because they act like they own the whole place. Now in urban areas of Hungary, most oncoming people will only glance at you for a very brief split second or not at all. It is rare for people to actually bump.
My experience was that if I concentrated hard enough while walking and juggling people, actually staring for a little longer anywhere where I assessed that an oncoming person would rather bump into me, or someone walking in front of me would not let me pass, they would conform to my visualized expectation of a fair movement, otherwise I was again like some wild deer or whatever from their point of view. I tried switching this on and off. It works. It is slightly different with people whose back is towards me than oncoming people who are sometimes ready for a brief conflict for space.
Then I saw my father, whom I haven't seen for several months. He is an ageing hyperconservative artist, who I think has some hidden psychic capabilities which he masks by all this negative obsession with politics, and he kept on explaining about how (figural) sculptures and pictures were "staring" at you and how some people - he referred to the vandals who broke sculptures, or the Russian soldiers occupying the country after World War Two, who holed the eyes of some paintings hung in the family living room for fun. He had a point.
After my meditation practice I noticed already decades ago that sometimes people would fail to note my presence in a room where I would normally be noticed.
My Guides conveyed to me that for years now I have semi-consciously tried to be much less noticeable, so if I wanted to be noticed I had to concentrate on it. I had thought this was an abstract thing - my political, spiritual and other pursuits warranted it - just like I have removed many items of personal data online, refuse to act in YouTube videos and use a fake name and birthdate on Facebook.
The vista opening before me was more interesting to contemplate - that this was a very general but overlooked part of human life, as relevant to everyday life as the unconscious when Freud discovered it, and that it was part of the larger scheme of human power systems. My beliefs obviously incite me towards mistrusting most kinds of political power and hence my overall "hiding" feeling.
There are many more interesting aspects that tie here - this is the very few venues I shared my study here. Briefly, I would use the term "personal power" in a very abstract sense to this. Now that has a different perspective when you start to contemplate it in a general scale...
If you wish, you could consult British biologist Rupert Sheldrake's partial research here:
Being stared at