This is a Banjo-uke, sometimes called a Banjo Ukulele or Banjo uke, which is a combination of a Banjo and a Ukulele.
There's more information, if you want to click the 'Banjo-uke' link.
They were first introduced by Alvin D. Keech in 1917. (Just after Bad Monkey House was built.)
This one was well beyond repair and so Mr. BMH made it into a light. Cool, huh?
It's already sold, but there are more if you are interested in having a one of a kind light of your very own, just drop him an email at Mr. BMH.