Thanks for the pointers, but I'm still confused. I wish I took a picture of it, but it looks like an air hose quick disconnect, like this:
The female part is sticking out of the transom, and I'm missing a hose that has the male part on it.
I'm thinking it might be something like this:
because I suppose "qd" means "quick disconnect" - but there is no picture of that hose, and the corresponding full shower kit:
looks like it might be a different connector.
Maybe I should drive the boat to a hardware store and see if I can try on some quick disconnect fittings to figure out exactly what size it is...