Faunce was individually selected to be honorary personal physician to five Prime Ministers (including Gough Whitlam and Malcolm Fraser) and six Governors-General (including Sir Zelman Cowen, Sir Ninian Stephen, and The Hon. Bill Hayden). Faunce was Prime Minister Harold Holt's personal physician at the time of the latter's disappearance in the surf at Portsea; his treatment at that time of Holt's shoulder injury and refusal to prescribe opiates featured in the 2008 film "The Prime Minister is Missing".