I think Stan's terminology could use some work. The way he describes the "long axis", "this axis", etc. could be confusing. What he dubs "the long axis" is the NORMAL of the ellipse. Imagine a pencil, placed upright on the eraser end, on the surface of your desk. The pencil then represents the NORMAL of your desk's plane. The "angle of the ellipse" is its MAJOR AXIS. Google it, and you'll know that the longest dimension of an ellipse is called its MAJOR AXIS. Now, from Stan's demonstrations, there's a possibility that you might get confused between the ellipse that is the actual cap of the bucket (let's called this EA), and the ellipse that is its REPRESENTATION IN PERSPECTIVE (let's called this EB). EB is only an approximation of EA at a particular angle of view, it is never truly accurate. Stan noted that he simplifies by making the NORMAL of EA PERPENDICULAR to the MAJOR AXIS of EB. The NORMAL of EA represents the forward tilt of the bucket, while the MAJOR AXIS of EB tells you how long you should draw EB and how you should orient EB. It is an okay simplification because the point of the lesson isn't to get too deep in the weeds of perspective, but since it's only a simplification, you may find it doesn't work well when you're tracing screenshots of the 3D bucket model. Just keep that in mind, it's only a simplification, and hardly a accurate one. Here's a simple illustration. The NORMAL is in red, and the MAJOR AXIS is in blue. In the most frontal view, the NORMAL is just a vertical line. As you orbit around the bucket, its tilt is increasingly apparent. The MAJOR AXIS is always perpendicular to the NORMAL, and it helps you orient the caps of the bucket and know their length.

Using ellipses to represent circles and ellipses in perspective is only a convenient approximation, hardly 100% accurate. I think a helpful way to think of circles and ellipses in perspective is to consider the squares or rectangles that inscribe them. Then you can use bisectors and diagonals to construct a more convincing ellipse.

What he was referring to as the "side-to-side" line is the "major axis" of the ellipse NOT in perspective. Basically if you draw an ellipse in 2D (x and y), an ellipse has a long axis called "major", and a short axis called "minor". As for the "line perpendicular to the long axis", that would be the "major axis" of the REPRESENTATION of the ellipse in perspective.

It's a livestream, and it's been barely a day seen it was streamed.