William J. Gau, consulting engineer in Johannesburg, was the son of Julius Gau and his wife Florence. In 1903 he became a member of the Geological Society of South Africa. A few years later he published "Geological notes on a portion of the Bushveld in the neighbourhood of the junction of the Elands and Olifants Rivers" in the society's Transactions (1906, Vol. 9, pp. 67-). This contribution earned him the society's silver medal in 1908 for the best original paper on South African geology by an author aged under 35 years. In 1906 he was a member also of the South African Association for the Advancement of Science, but his membership had lapsed by 1910.
Gau served as joint vice-president of the Geological Society of South Africa in 1922. With J.I. Jameson he presented a paper on "Tin mining in South Africa" at the Third Empire Mining and Metallurgical Congress, held in South Africa in 1929. The paper was published in the Proceedings (1930, Part 3, pp. 197-236).
Gau married in May 1908 and was survived by his wife, Jeanetta Eleanor Hollins Gau, born Palmer, and two children.