[Legate of Amon Lanc]

Interesting question at least!

I think I have had, always, a sort of unconscious answer to that - like, I was never trying to form any definition consciously, but now that I think of it it makes sense - that simply it is a certain quality, a "metaphysical" one if you wish, a sort of invisible stamp which then the others can perceive, if they are a) truly perceptive, b) an Elf (or a Maia, or something like that - something which is "metaphysically perceptive" in this sense). I think many people would actually at least at some points be able to distinguish that "there is something strange about this person" if they met an Elf-friend, only they wouldn't be able to understand what exactly it is. The status of the Elf-friend in general would mean that the good powers (whatever exactly that is) will watch over the person a bit more as well. Perhaps we are talking some Elven "guardian angels" who don't usually meddle with mortals, but if such a "guardian angel" happened to be around when an Elf-friend gets into trouble, it could intervene. That's rather roughly said, but I hope you understand what I mean: things in Middle-Earth don't happen "by chance", and for an Elf-friend, there could be somewhat bigger chance for having "good luck" in troublesome situations (in the sense of meeting a friendly Elf-patrol when lost in the woods, when pursued by a bunch of Orcs, or stuff like that).

However, one thing I would like to clarify - I don't think this "perceptiveness" would be a matter of some "spiritual power", i.e. not that every Maia, for example, would be able to immediately recognise that you are an Elf-friend. I don't think, for example, that a Balrog would, or that Sauron would, or that the Nazgul would. At most, they could be afraid of some air of power around you, if they threatened you, but they would not be able to say its source, whether it is that you are an Elf-friend or that you happen to own one of the Three Rings. But I think actually, you would be able to perceive an Elf-friend the better the more, if I say it in a very crude way, "good" or the more "pure in heart" you were. (Except the Elves would, likely, be able to perceive it regardless of their personality. Dúnedain would be able to perceive it only a little bit better than normal people, still not always.) So basically, yes, almost all Maiar would be able to perceive this "stamp", as they are both powerful and "good", but then Sauron and co. would not, and Saruman would perhaps have realised at some point between 2000-3000 TA that he cannot see that so well anymore, or even a) he would not care that much anymore, b) he would start to think (if he ever concerned himself with such a matter) that Elf-friends are simply "dying out" because he hasn't seen one for a rather long time (not realising that he can't). It could even lead him to a false impression that Elf-friends don't exist anymore - therefore supporting his theory that also the time of Elves is over, as they have nothing to do with humans anymore, the two races are estranged (no Elf-friends). I think that would be a prime example of this blindness drawn from the belief in one's own omniscience - and very fitting for people like Saruman.

Last remark. Note the interesting cry of the Orcs in the Hobbit, "Murderers and elf-friends!" I think the knowledge of that something like "Elf Friend" exists got outside among other races as well, but they still were not able to perceive it. I think among the Orcs, this honorable title eventually became a swear word. So that's just to say that I don't think the Orcs were "perceptive" (they had to see the swords of Gondolin, after all, to realise that. Apart from it, Thorin and co. really weren't Elf-friends - only Gandalf likely was, and Bilbo got that title much later - and not sure if they would even like to accept such a title, at least most of them. Did Gimli do so, by the way?).

All of what I have said is my personal theory: sort of formulating in words what I have been more or less thinking all the time. But I think it fits (at least for me) and is in tune with how I perceive Middle-Earth and its mechanisms, so to say. Of course now people can see if they have different perception of M-E, if this does not fit their image.