(n.) a glossy, chequered fabric; a tortoiseshell cat
A calamanco is a tortoiseshell cat.
As grand as that word is, alas its history is somewhat muddy and largely unsolved.
As a name for a tortoiseshell, it appears to have fallen into use by the nineteenth century. Before then, calamanco was the name of a type of glossy, chequered fabric produced in Flanders, and in that sense the word first emerged in English (perhaps borrowed from Spanish, or Italian) in the mid 1500s.
Calamanco fabric is unusual in that its characteristic chequered pattern is only visible on one side, and that quirk was enough to not only establish the word in our language, but make it a memorable point of reference for anything similarly chequered or mottled.
So calamanco language is an indecipherable patchwork of random words. A calamanco person is someone with a muddled heritage, or else who speaks in calamanco language. And a calamanco cat is one with mottled, tortoiseshell patterned fur.
As for where the word itself comes from, that’s something of a mystery—but the best theory we have is that it is in somewhere descended from calamaucus, a Latin word for a soft hat or skullcap. Perhaps this fabric was once particularly used to make such headgear? Or perhaps the two share a common ancestor now lost to the etymological mists of time, and are otherwise unconnected. Without further evidence, unfortunately we can only guess.