Tom, the Simplex Scooter was built from 1957-1959, I believe. I have read where some might have been built in 1956, but I don't know much about these scooters.
In 1939, Simplex built a scooter that used the wheels, front suspension, and engine, but with a step thru frame for delivery service. I have never seen one in person, but have seen a picture or two. I think Gary Wollard had one in his collection, and he wrote that they came in 2 different wheelbases. If I find a picture, I will add it to this post.
Was that scooter you saw for sale? Did it have an engine?