That factory tire carrier was never installed on any Land Cruisers delivered new to the U.S. market.
Since the last 80 series was produced in 2008 under lic. in Venezuela.
Which was the only country still producing the vehicles after production ended in Japan in 1997.
Once the production line stops, soon afterwords suppliers stop receiving orders to make replacement parts.
So once existing inventory in Toyota's spare parts supply chain is exhausted, that part will become NLA.
Since i wrote that post almost 4 years ago, I'm thinking that if you can't locate it on that web site, that part may now be NLA from Toyota as a new part.
Seeing as you live in Australia, and that was a market where that style tire was delivered, I'd look for a used one in a local wrecking yard.