OK Flatlander, both the Moor and Spanish connections immediately made me think of Sardinian, so I did some wandering through the online Sardinian dictionary (quite difficult since I don't know Sardinian and that which I know is not the same "branch" as what most of the dictionary is written in). And I got (struggled with translating the definition):

Tabbiche or tabbicu: A layer of wall, thin wall, of half(?), made of brick or other, also of [some kind of] canes.

So it looks like it's a wall-word, but you'll have to wait until I can ask my live Sardinian dictionary (aka my father) if he knows such a word, and what he knows it to mean.

Thanks for the fun challenge!