If you were to be uncivil enough to describe somebody as a dog’s tail, that person would almost certainly be offended. Changing the epithet to cynosure would evoke the opposite reaction, since the latter means a person at the centre of attention. And yet in origin they’re the same.
The connection is astronomy. Like other ancient civilisations, the Greeks were familiar with the star we now call Polaris. It lies at the end of a constellation that we sometimes call Ursa Minor (the little bear) or more colloquially the Little Dipper, with the handle of the dipper having the star at its end. Greek mariners called the handle kunosoura, dog’s tail, from kuon, dog, plus oura, tail. They also attached the same name to the star itself. At the time it wasn't the pole star, but one of a group of three bright stars near the pole that served the purpose.
(The dog’s tail should not be confused with the dog star, Sirius, which was given that name because its constellation of Canis Major (the Great Dog) seems to follow at the heels of Orion the hunter, as does his other dog, the constellation of Canis Minor, which contains the lesser dog star, Procyon.)
The name was taken into Latin as cynosura. From there it moved into French and eventually into English — as cynosure — at the end of the sixteenth century. The meaning at first was of the stella polaris, the pole star, since it had by then moved nearer the celestial pole as the result of a wobble in the earth's axis. In 1596, Charles Fitzgeoffrey wrote in a book about Sir Francis Drake: “Cynosure, whose praise the sea-man sings.” He also used it figuratively for a guiding light. Within a few years people transferred it to something that was the focus of attention, as the pole star was to seafarers. It was only a minor step to using it for any focus of attraction, interest, or admiration.
We still use it that way, though it has so often fallen into cliché as the cynosure of all eyes that wise writers have to be careful of it.