Hi Joe and Rich,
While I have no documented evidence about the song, it comes to me through family sources. 'Los Bilbilicos' was believed by my parents to be Ladino in origin. My paternal grandmother who came to the US in 1905 learned it in Istanbul before the turn of the century.
It sounds 17th century or so to my ear but that's a WAG.(wild-ass guess)
Farina used one version of the tune but wrote his own lyric unrelated to the Ladino. Other tune versions sound more Oriental and modal. I'll warble other tunes for it at you sometime, Joe. You too, Rich if you happen to be in Northern California