I reckon the key to working with ellipses is visualizing where the "implied cylinder" is, as a guide to how to orient the minor axis of the ellipse template. What's that mean? Imagine a plate on a table in a one- or two-point perspective drawing. Now imagine a cylinder of equal width projecting straight up and straight down from the plate. This is the implied cylinder. We would make the minor axis of our ellipse template point straight up and down to conform. The video explains.
The attached videos cover a slightly more involved example, in that here the implied cylinder points toward a VP. (The car is drawn to a particular pair of VPs so the wheels must be too. Perspective is all about relating like to like--that is, one thing to a similar thing, such as the left rear wheel of a car with the right rear or left front wheel.)
(BTW, for simplicity the front wheels are pointed straight ahead in this example.)
Another note: My red underdrawing reads too strongly in the final videos. I'm sorry. Try to ignore it--your attention is best directed instead to the black pencil lines.