@AlanJaffe,
Your question is not directly related to this thread which talks about rotating video a discrete 90° turn in order to get vertical video to display correctly in a horizontal view.
What you are talking about is the Visual Effect called "Spin 360°". When applied to a clip in Movie Maker, it begins spinning the clip while gradually zooming out and then eventually back in once it has made the full 360° turn. Unfortunately, there isn't
a provided way to modify any of the Visual Effects so your only option is to live with the behavior given in the standard effect.
Alternatively, you could find a clip that has an eyeball that is already doing a 360° spin or find an animation program that would let you take an image and spin it around that way to create a video. But just using Movie Maker, you cannot achieve this look.