Centaurus - I'm sorry, in the fog of much information overload, I found the story I read... and it's not the story you're looking for.
It was the story of the Wackett trainer VH-BEC that ran out of fuel and landed on firm ground between sandhills, in Northern S.A., about 200 miles North of Cook, in 1962.
My memory is totally faulty on this one... unfortunately, this pilot wasn't found in time, and he died of dehydration. The search was carried out by 18 aircraft, but the search was eventually called off.
A Hudson, VH-AGE, of Ad-Astra Aerial Surveys, found the Wackett by accident over 3 yrs later, and the story is on the Ad-Astra website.
ADASTRA AERIAL SURVEYS - The Missing Wackett Vol. 1