I've never seen one of those before!
I suspect it originates from a couple of decades before 1960.
Google reveals similar things in Canada that sold on eBay.
At least one ad describes it as a 'pressure switch', but probably they just mean 'push button' switch.
I think it's a novel 2 gang light switch from the era.
It sounds as if it was wired to connect the two lamps in series in one of the positions, to give the half intensity effect.
Is there a brand name or patent number marked on the base underneath?
View attachment 119718
Reply to the thread, titled "Unknown switch" which is posted in Lighting Forum on Electricians Forums.