He was the fourth son of Robert and Bridget Brocas (née Taylor).
Brocas studied at the Dublin Society's Drawing School, winning prizes in 1772 and 1773.
He went on to become a portrait and miniature painter from his home, 64 Dame Street, Dublin.
An advertisement for his services appeared in the Freeman's Journal on 28 February 1778, announcing his return to Dublin.
He died in September 1780, and was buried in St Andrew's Churchyard, Dublin.