Heads that are ambiguous in the sense that they can be read either way up are another illustration of the salience of faces for the brain: features which are a key facial element one way up almost disappear when they don't really fit in with the face that appears with rotation. It's curious to take a look at heads like these exactly half way between one way up and the other, as shown to the left: at this point, both heads appear, but still only one at a time, so that the image is unstable, and crown and chin flip from side to side.
These heads were a popular feature of nineteenth century books full of puzzle pictures. A beautiful collection of these is Julian Rothenstein and Mel Gooding, The Playful Eye, (Redstone Press, London 1999).
It includes a whole section on rotating heads, but also some frames from one of the American Peter Newell's brilliant, almost surrealist comic strips, Topsys and Turvys of 1893. In his stories, the second half of the whole comic strip is simply the first half turned upside down, so that you end up on the inverted starting picture. Another cartoonist of a century ago taking advantage of the same idea was Gustave Verbeek. There's a post about him on my illusions and aesthetics site at www.opticalillusion.net/optical-illusions/gustave-verbeek/
To draw your own rotating heads, start with the eyes, and then add other features one by one, trying the effect of each both ways up.
In comic book picture 4, The Genies, the genies share a single head like this. They just don't both use it the same way up. To draw your own rotating heads, start with the eyes. Make sure they don't look just the same both ways up. Once they have a different expression one way up from the other, you can add features gradually.