Like Penny Heyns, Gary hails from Amanzimtoti in Natal, where he swam at the Kingsway High school and competed for Amazimtoti surf lifesaving club.
In 1981 and 1982 he won the Midmar Mile. At the South African swimming championships in 1982, Gary won three gold medals.
In January 1983 Gary Brinkman took up a scholarship and joined fellow Springboks Erwin Kratz and Gerhard van der Walt to swim for the University of Southern Illinois, and by 1984 he had already won a US national swimming title. At the US nationals in August he won the 400m freestyle in 3:55, 24.
Admittedly the top US swimmer at the 1984 Olympic Games 400m freestyle finished fourth in 3:48,09. Gary felt the loss of being excluded from the Olympics keenly.
In the summer of 1986 Gary Brinkman was one of two swimmers to take three titles at the US National Championships in Santa Clara. Teaming up with fellow South African exile coach Jonty Skinner at the San Jose Aquatics club, he won the 400, 800 and 1500m freestyle events.
He moved to Australia after he graduated in 1986. On the Gold Coast of Australia he swam with coach Bill Sweetenham at the Australian Institute of Sport.
In Australia he continued to swim in Queensland. where he hatched a plan to get to the Olympics in 1988. He married an Australian to get Australian citizenship. Unfortunately the Australian government objected, and despite marriage, he was ruled ineligible to swim for Australia. He eventually did manage to win that right - in 1992, when he did not make the Australian team to the Barcelona Olympics. He might have made the South African team, which had no 1500m qualifier. In 1994 an Australian film "Muriel's wedding" was based on this storyline.
1982 Mainstay 3,2 km surf swim. Gary Brinkman shares the podium with fellow Springbok swimmers Kevin Richards and Tricia Butcher, and Surf lifesaving Bok Julian Taylor.
In April 1984 Gary won the 400m freestyle at the US swimming championships in 3:55,24. His winning time at Pretoria in 1982 was 4:10,79.
He also took third place in the 1500m freestyle in 15:36, considerably faster than the SA record held by Simon Gray at 15:58. Gray's record was only (officially) broken by Ryk Neethling at the SA Championships in 1994 - in 15:56,66.