Alan,
You describe the way I go around, looking for images. Something appeals and we stop to look.
[May we discount seeing something that already interests us? I don't wish to denigrate anybody's area of interest, but a bird-watcher or a steam engine enthusiast will always stop for a rare bird or engine, where an ordinary person might give a glance and pass by on then other side.]
As you say, it seems to be unconscious, but it also seems to be better developed in some people.* My experience is that something attracts our gaze and we prepare to take a picture. One part of the preparation is setting up the tripod or raising the camera to the eye but the other part is inspecting the scene more closely. The limitations of LF oblige us to observe more intently than an iPhone user, who carries a virtually unlimited supply of dark sides.
When we are set up, it's my experience that the process shifts from reactive to analytical. Should that object at the edge be included? Do I want more sky? Will a filter help? Is this the right lens? Should I open up to get a faster shutter speed? It's always possible that an intrusive branch, intrusive people, inappropriate lighting or the lack of a place to stand will make us abandon or postpone the shot. We can all fill in this list. We've all been there.
* I did once come across someone who had no sense of composition. We needed to make simple records of a large number of pack designs which we sent out to a studio. At the same time, we had an artwork studio, with a technician who maintained the equipment, but was not always busy. I set up a neutral-coloured scoop with a large light-source above so that any object could be put there and recorded faithfully. I ran off the first batch of slides, both of individual products and groups, with the technician observing. Then I handed over to him. He was entirely unable to arrange a group of boxes. If they were within the frame, than that seemed enough to him. Mine seemed better in some way, but he couldn't see what that difference was. He was not a stupid man at all and he was not unwilling, so I was baffled. I still am. How could he not see?
(Even more amazingly, I once came across a woman who didn't like chocolate, but that belongs on another forum, if there in one.)