In the Latin literature of the late Middle Ages I have found a very interesting development of the use of the word "occultatio", away from a rhetorical one towards one involving light and darkness. Originally, occultatio means "the act of putting away or of hiding something". One finds it most often in the sense of "hiding a truth" or of "hiding oneself" (Caesar in De Bello Gallico, Cicero in a letter to a friend, Arnobius in Adversus Nationes, Tertullian in De Paenitentia). This continues beyond the so-called dark Middle Age: Aelred of Rievaulx, in his famous De Amicitia, still uses occultatio in the sense of "dissimulation", "hiding your thoughts".
But in a sermon by Albertanus of Brescia (c. 1195 - c. 1251) I found this phrase:
Occultatio vero luminis removeri debet, quia, ut ipse Dominus ait: "Nemo accendit lucernam, et ponit eam submodio, sed super candelabrum, ut luceat omnibus, qui in domo sunt."
To a concealment of light, however, one must put an end because, as the Lord himself sayeth: "No man, when he hath lighted a candle, putteth it in a secret place, neither under a bushel, but on a candlestick, that they which come in may see the light."
Taking it from there, the great Zingarelli dictionary of the Italian language signals the use of occultazione, in the astronomical sense, as being extant since the year 1328. For the English language, the Oxford Dictionary of English Etymology says the word occultation, again in the astronomical sense, to have been used "since the XVIth century", without giving a quotation.
So the hypothesis seems warranted that preacher Albertanus of Brescia laid the groundwork for a new use of an old word; that from there this new use passed into what, later, would become the Italian language (modern Italian is an evolution of the Tuscan dialect; Brescia is in Lombardy, and the dialect of that region has had strong influences in the genesis of modern Italian) and that from the Italian, it found its way into English. It's nothing more than an hypothesis, though supported by written documents.
NB: the quotations given without an online source come from hard-copies in my library.
Edits: spelling, formatting, NB note, precision on the genesis of Italian