We find from Egil’s Saga, ch43, that about AD900 ‘Bjorn Hairld of Aurland in Sogn, who had fled from the fiords with Thora Hladhond, sister of Thorer Herse, was wrecked near Moseyjarborg’ (Mousa) and took shelter there until his ship was repaired, and he could continue his voyage to Iceland. Again in 1154, Erlend Junge, a chief from Hjaltland, fled with Earl Harald’s mother, Margaret, widow of Madadh of Atholl, and shut himself up in Mousa, where he stood a siege (p342 in the Orkneyinga Saga). Neither of these notices, however, necessarily implies that the broch was at these dates owned or occupied by any one, but rather the reverse.
Cribbed from
IV.—The Brocks or “Pictish Towers” of Cinn-Trolla, Carn-Liath,and
Craig-Carril, in Sutherland, with Notes on other Northern Brochs,
By the Rev. J. Maxwell Joass (c1871)
online here