Nathan, Briggs did not make 2 strokes. They struck a deal with Komatsu Zenoah to do that for them. Then it turned out to be financially unviable so they stopped after a couple of years.
I do not think the engines are rare, but if you wanted one you'd have to expect to go looking for it rather than pick one up from a nearby tip-shop. I have the impression it is quite a good engine, comparable with a Suzuki or Kawasaki.