Mr. West ...
The author uses a close-range perspective effect to match the Moon. There is little doubt that holding something very near to one's face or camera can create lots of angles. Yet, in the first far distance scene the illuminated portion of the ball points at the Sun. It is not until the observer gets up close to the ball, to a special carefully selected position beneath it, that the ball is able to point away from the sun, in a similar direction as the Moon.
So we see, the phase of the ball does not behave in the same at all positions. One must carefully select the position of the camera to match the Moon.
The observer, without the ball, can look at the Moon, or the Sun, or points elsewhere. If he looks at the Moon, he is looking along side CA, toward A; if at the Sun, along side CB, toward B.
The only place to hold the ball in order to see if its phase matches that of the Moon is ON side CA. If you hold it elsewhere, at any of the "other angles" or "other positions" that you refer to, you've instantly defeated the whole point of the exercise.
Since it is impossible to see
through most ping-pong or golf balls, the observer must hold the ball slightly off from the line of side CA in order to see both the ball and the Moon. If it is held perfectly ON the line, it will obscure the Moon.
OF COURSE the phase of the ball will vary if you look at it from different places. If you look at it from between it and the sun, from a point along side CB, toward C, it will have no phase, and all you will see is the lit surface. If you look at it from outwith the triangle, from a point extended along BC but "behind" the ball with respect to the Sun, all you will see is shade. The phase will vary according to the angle at which you view it, and will only match the Moon's if you hold it such that you are viewing it AND the Moon from the same angle.
The whole idea of the exercise is to observe the ball from the same angle at which you are viewing the Moon.
Your lamp posts from a page or so back (currently #74) only line up if you stand in line with them. Clearly, if you stand elsewhere, they will not line up. Clearly, if you do not align your line of sight with the ball AND the Moon, they will not appear to have the same phase.