Thank you Frances for pursuing the meaning of Beal y Vair and for introducing me to Broderick's "Place names"
Vair is not in my elementary Manx language book.
Beal has the same meaning & pronunciation, in my slightly more advanced Scots Gaelic book, but the spelling is slightly different.
The is no letter "V" in Scots Gaelic - Bh & Mh substituting.
.a' Mhuir pronounced voor - the sea -sounded most likely.
In the absence of a more informed opinion, I consided the name might refer to a natural geographical feature.
Perhaps a narrow cleft providing drainage from the headland, down the cliff face widened by erosion into a mouth where it reached the sea.
Fanciful & wide of the mark.
Harry.