I mean, obviously, one would certainly not expect there to be an electrical box behind the vanity light. That’d be crazy. Clearly, conduit and a metal plate are all one needs to mount a light.
For that matter, it’s TOTALLY normal to sauder? weld? permanently join in some fashion, a sink drain pipe directly to the surface of the tile under the sink. Because, really. There need not be an explanation for such obvious choices.
Again I say, I can’t make this stuff up.
In good news, the vanity light is now installed (with an electrical box thankyouverymuch), the walls are painted ($2 oops quart was plenty! Whew!), and the (second) sink hasn’t fallen!! Progress!