Dance by the Light of the Moon was written and performed by the American doo-wop group, The Olympics.
The group released the song in 1960 and it topped the charts at #47.
This doesn’t seem to be as well a known song as Fly Me to the Moon, Moon River, Blue Moon, Moonlight Bay, By the Light of the Silvery Moon, Shine On Harvest Moon and Blue Moon of Kentucky.
No other information has been found on this song so far.