I'll bet that's the same frame as my first Schwinn, which was probably from the early 1950s. Mine had a 2-speed Bendix coaster hub and a shifter which looked like a brake lever. The fenders on mine were painted black, instead of chromed.

That stick shift is sort of cool, as long as one does not slide forward into it during a mishap. ... What I like even better are the small old school Sturmey Archer top tube shifters, which are pretty hard to find, and which would probably look out of place on a Schwinn.