Upon leaving the School, Gillon went on to study medicine at the University of St Andrews where he qualified with his MBChB in 1960. After taking up various training positions across Scotland,
he then began working at the Royal Brompton Hospital in London.
Come 1970, Gillon was appointed as a Consultant Physician with an interest in chest medicine at Northampton General Hospital. Here, he played an instrumental part in the local transition of
chest medicine into an integrated and essential part of acute hospital services. He oversaw the introduction of fiberoptic bronchoscopy, respiratory function testing and asthma nurses, as well as
beginning a swimming club for children with asthma.
In 1976, Gillon became a Fellow of the Royal College of Physicians of Edinburgh and just four years later became a Fellow of the Royal College of Physicians London. He retired in 2001, although he continued, for a period of time, as an examiner for the Edinburgh College of Physicians.
Gillon was described by those close to him as a polymath, with a true passion for English and Scottish literature, classical music, history and visual arts. He also maintained a love for Latin and Greek texts throughout his life as well as a deep knowledge and keen interest in the railways of the United Kingdom and Ireland, and of the passenger steam ships of the Clyde. Gillon also wrote a history of the SS Waverley, the last surviving paddle steamer on the Clyde, and was elected honorary Purser.
Passing away peacefully on 20 March 2017, aged 80, Gillon is survived by his beloved wife, two daughters and three granddaughters.