I assume Brian has his answer from other sources, but for the rest of us I've borrowed the James Gullan book 'AS LONG AS IT HAS WHEELS' - self-published back in 1993.
Turning straight to Chapter 6 The Ballot Oldsmobile, it mentions this early within the first page "Then one day a friend told me he had seen a Ballot car for sale, at a garage in South Melbourne. As I had only ever seen the two Cooper Ballots, I found it hard to believe until the radiator badge was described as having an Anchor on it. We went down in the Ford, bought it for 15 pounds, and Christine towed me home."
The Chapter then describes how tired it was, how parts were onsold (engine for a Bugatti special) and how basically all that remained of the car in its special form was the Ballot name for registration purposes. The Chapter also gives a rundown of events he ran the car at.
The list of other cars that came his way also makes an interesting list - GP Salmson, Wolseley Hornet special, Austin special, GP Ballot, Stutz Black Hawk, Ballot Ford, V8 Hot Rod, Zephyr special, GP Alta (raced in the UK), several early MGs - inc K3 and several more interesting, but more modern cars of the 50/60s. Some used for competition and then there's his drag racing era.
A potted history of James Gullan's life with cars was published in issue 62 Australian Muscle Car magazine in mid 2012.
In the February 1994 Rob Roy Hillclimb programme there's a page dedicated to James Gullan and Bill Leech. Both had recently passed away. For those interested James is recorded as having died of a heart attack aged 79, early Friday 21/1/94.