I just replaced 3 bathroom fixtures with those type. Mine came with a built in glass lens/shade. I think it has a better seal in wet applications like in a bathroom or shower. Halo E26 Series 6 in. White Recessed Ceiling Light Fixture Trim with Frosted Glass Lens, Wet Rated Shower Light 6150WH - The Home Depot
Yes my 1977 Merc has one. But remember the motor in question was converted to electric start aftermarket. Might not have a kill switch.
I would check fuse, ground, switch, starter.