This past weekend, while researching Beutler for the NEH 2406 puzzle, I ran across a blog (which I can no longer seem to locate), which indicated that Beutler had a program for producing custom cars, first on VW chassis, and later on Porsche chassis. I seem to recall that a Porsche chassis mentioned was the 944, and the Beutler/Porsche product, called a 944SC (not sure about the trailing letters), was offered in the late 50's/or early 60's. Apparently at least one, or two, cars were actually manufactured, as the blog conversation was centered around where any surviving Beutler cars were located.
Anyway, I'll propose that the car depicted in the drawing for this puzzle is a: 1958/1962 Porsche 944SC (sp?) by Beutler of Thun, Switzerland.