Lughaidh wrote:
It may come from "bríste" with an added -s by analogy with the English words (that are plural) that mean "trousers": trousers, pants etc... (for an English mind, trousers are a pair of things). Because Irish bríste and Scottish briogais are singular

I'm thinking of the Scots "breeks", though. "Breeks" and "briogais" are almost definitely related, and it seems more likely that it went from Scots to Gaelic. A lot of islanders will slenderise the -s if they're embedding an English plural form in their Gaelic. Old writing also suggests that the -s ending would have been a full syllable (or at the very least preceded by a svarabhakti vowel).
If it was "bríste" in Irish that was the source, I can imagine the S migrating to the second syllable in an Anglo-Saxon language, but it would be odd in Gaelic, wouldn't it?
So "breek-ess" is a very likely form in Early/Middle Scots, while "briogais" is a very unusual form for Scottish Gaelic...