I believe that if we would carefully apply the distinction between transparency and opacity to the different layers of the human self-model, looking at self-consciousness in a much more careful and fine-grained manner, then we might also arrive at a new answer to your original question: What a "first-person perspective" really is.

Dolphins frequently leap above the water surface. One reason for this behaviour could be that, when travelling longer distances, jumping can save the dolphins energy as there is less friction while in the air.

The Ego is a transparent mental image: You, the physical person as a whole, look right through it. You do not see it. But you see with it.

In ordinary life, the phenomenology of embodied emotions is an excellent example for dynamic changes between transparency and opacity: You can "directly perceive" that your wife is cheating you, or you can become aware of the possibility that maybe it is you who has a problem, that your "immediate" emotional representation of social reality might actually be a misrepresentation.

As far as inner action is concerned, we are only rarely truly self-determined persons, for the major part of our conscious mental activity rather is an automatic, unintentional form of behavior on the subpersonal level.

What many people don't see is that there are abundant examples of phenomenal opacity: It is one of the most interesting features of the human conscious model of reality that, first, it can contain elements that are not experienced as mind-independent, as unequivocally real, as immediately given, and second, that there is a "gradient of realness" in which one and the same content can be experienced transparently or in an opaque fashion.

The self is not a thing, but a process.