OK, I talked to Vaughn, and he talked to Ian McDonald, leader of the 1969 expedition team, who is just getting over Covid. So for the first time anywhere, here are the details of how the team navigated.
They had a Nova-Tek Non-Directional Beacon (NDB) Finder fitted to Rhino, one of the CJ-6 Overlanders. It can just be seen on the dash in front of the gearshift, in this photo of Ian in the Jeep. Ian is using the Royal Flying Doctor Service two-way radio (call sign 9QLG). A floating compass is near the top of the windscreen.

There was an NDB installed at Andado on the western edge of the desert, and Ian and his crew were able to connect to this NDB with their beacon finder each night. An NDB does not give co-ordinates but when a finder connects to it, it shows the direct line between the beacon and finder. Gordon Gant would then take a reading next morning with a lensatic compass and that would determine the route for the day.

Due to their zigzagging it was necessary to take daily readings from the NDB to ensure they did maintain a westerly direction to Andado. The compass on the windscreen was used during the day just as a check to ensure they were not straying too far off course.
Thanks for the question, Rus. I will add this to the article on the website.
Derek