I thought that turn signals were not a factory option until 1960, but it looks like they actually started offering them in 57. From what I can tell looking tonight, it appears that GM offered the same switch that the Corvettes used as an option then.
This is probably actually a correct switch/housing, I just have the wrong steering wheel.
It appears that this setup (assuming it is the parts I think it is) did not have a latch/cancel. The internals are a pair of levers and springs to center the stalk and you had to pulse them yourself.
I kind of like that as an "unusual but original" feature. I think I will try and fit it as-is and keep it as a curiousity.