Wayne,
That 'other' need be noone but oneself. We should indeed be the audience we are playing to.
That ("self-exploration") is the only way we can have a style at all, without it being a imitation (i.e. not ours).
'Style' is indeed something that only comes to light when something is perceived.
Assuming we (the original creators, who's idiosyncracies reflecting in the created work), seeing/perceiving what we do does not count as such, then you could perhaps raise the question about whether it is there or not. (And there is an answer to that, but...)
But that would be rather far fetched, even for a play with simplistic logic (like that 'old' falling tree thing).
So should we waste time thinking about thingies like this? I think not.
As we are indeed dealing with a form of expression, 'style' will be 'compromised' by the anticipated reception the expression will get in a wider audience.
We will adjust our expression to perhaps maximize the 'effect'.
That adjusting can be as extreme as adopting the style of someone else, who we know is 'in favour' at the moment. Imitation.
But at the very least being directed at a particular audience will leave its mark (to make sure i get my message across, i'm now writing in English).
Does that mean that style never is just a personal thing? Perhaps.
Perhaps we never are the 'personal' persons we personally would like to think we are, always taking part in a 'social'/communal thingy.
Yet, as long as we can say "i" and "they" ("me" and "them"?), we will suffer the delusion that style, to be not just an imitation of "how others do things", is (must be even) a 'personal' thing.
(After all, if style is not our unique (!) way of doing things, who are we imitating? And how can it be that there is a truly original 'style' for us to imitate, without we being able to have a truly original style ourselves?)
So style is, like so many things, not one definite thing.
But that's all only looking at the intentional part. There is, of course, another, 'coincidental' part.
For instance, people have a tendency (or rather, in these days of auto-everything: had) to interpret what light meters are telling them either "optimistically" or "pessimistically", consistently rounding metered values towards one particular end, up or down. The results will show that.
Just as other unintentional behaviour, 'habits' grown out of convenience, or whatever, will make itself noted. These things just 'grow' quietly, until someone notices how consistently the same thing shows itself.
For professional photographers it is best to not have a personal style (or rather be able to 'turn it off'), and to be able to produce work in any style required.
Just like a professional copy writer must be able to use language the way that is required by the job in hand, and must keep his/her personal 'style' for that novel-that-will-upset-the-literary-establishment being written after hours.
That is, unless you are at the very top of the business, and can wallow in the luxury of people coming to you, paying heaps of money, to have you do 'your thing' in 'that way noone else can' (they of course can, but don't get payed as much for doing so because it is mere 'imitation', not the 'real thing'. Yet very professional...).