Meaning and determination of Stand Point in Perspective Drawing

In his Complete Guide to Perspective Drawing, Craig Attebery defines the concept of Station Point as the following:

Later on, the author tries to represent this Station Point in a picture plane, acknowledging the obstacle of representing it and proposing a circumvention.

CV = Center of Vision

HL = Horizon Line

This circumvention gets even more curious when there are three vanishing points: right, left and vertical. In this situation, three station points are placed, each linked to a vanishing point and all connected through a compass. As impressive as it may seem, the author states they are the same point:

One, three or infinite station points, this construct does not appear, at first glance, to make sense. The eyes, after all, are at the height and length of the Center of Vision, not left, right, below or above. Still, Station Points are useful for drawing angles, as in this example:

For these reasons, I would like to know why this circumvention for representing Station Points is valid. Both formal and image proofs are welcome.

Suppose the viewer is looking at some object (a red sphere in the diagram below) in the distance. He perceives it to be at some angle $\alpha$ to the left of the centre of vision. Now take the triangular flap in the diagram and fold it down onto the picture plane. The station point is where the viewer's eye lands.

The key observation is that the angle $\alpha$ remains unchanged as the triangle swings down. Therefore, given the station point and any horizontal angle with respect to the centre of vision, we can reconstruct where it should appear on the picture plane.

The most convenient station point is the one directly below the centre of vision (or directly above, which is really no different), and that's because the viewer's gaze is parallel to the ground. We're typically interested in angles to the left or right of centre. However, if the gaze is tilted, or if the scene has some complex geometry, then it becomes necessary to use a different station point: the idea's the same, but instead of measuring along the horizon, we're measuring along another axis. In general, there is a circle of station points on the picture plane, each corresponding to its own axis.