It is direction of light source. As stated before, move your light source to the front of the ball.

I am uncertain why you think paths around the Earth, length of cycle, or the equator is relevant.

Simply imagine a line from the sun to the moon in the sky. That is how the light should behave and reflect from the sphere that is the moon.

Did you not review the video in the link? The refection causes a hot spot, as in the above image, and not a crescent, as often occurs. With no interference from the Earths shadow.

It is direction of light source. As stated before, move your light source to the front of the ball.

I am uncertain why you think paths around the Earth, length of cycle, or the equator is relevant.

Simply imagine a line from the sun to the moon in the sky. That is how the light should behave and reflect from the sphere that is the moon.

Did you not review the video in the link?