Quote
from the illustration it does look like the plug pins are of round section, rather than flat.

I think the illustration is showing the prongs edge-on. I'm sure the accompanying patent notes would have specified the shape and size.

Quote
It was common in Australia up until the 1950's to still be powering appliances from a light socket.

Ditto in the U.K. You could get both a bayonet-cap plug to fit directly into the lamp socket, or an adapter to convert from BC to a regular 2-pin 5-amp round-pin socket.

One rather bad consequence of was that the many people who wanted to use an electric iron from a convenient overhead light would often just leave the earth wire hanging.