But as you see from the quotations, and which I earlier mentioned for just this reason, 'borax' first occurs in 1944, a hundred years after 'borak'.

When I earlier mentioned the OED's reference to 'barrack' and said I couldn't see a connexion, I refrained from adding details. They say to see the EDD. So I did. There's a Northern Ireland word 'barrack' meaning 'boast, esp. of one's fighting skill'.

The original meaning of the word 'barrack' = 'cantonment' is a soldier's tent or booth. Ultimate origin unknown -- Spanish, from unknown earlier language (OED suggests Celtic and one or two others). But that could give rise to 'boast, swagger like a soldier'.

On the other hand there is also 'bark' extended to various noisy senses, including 'crow, boast' recorded from WYorks in the EDD. I don't know whether it's phonetically plausible to derive 'barrack' from 'bark'.