Googling that part number got lots of hits for me just now. However, perhaps if you have already tried all of them they might have then replied to you with "on back order". When that happens, ask them what the promise date is (the system will respond to them with a promise date).
When faced with your scenario, where some sites indicate a part is NLA or on BO, I've tried reaching out to every one of the dealers that indicates on google they can sell it, and then see if any will come through.
Also, there are different distributors in each region (and because they are separate businesses they don't always communicate to each other perfectly): in the US you can go through online dealers, but note the ones in Texas or Florida are each separate from the rest of the nation, so its worth trying dealers in those states (Texas is Gulf States Toyota and Florida is South East Toyota, and each of those regions is separate from the national TMS distributorship).
Then, try offshore, Japan Parts Online, and MegaZip for Japan dealer warehouse search. Note MegaZip includes UAE (the ME central warehouse). Because the FJ is still sold new in the Mid East they may have lots more parts on hand.
And try Japan Parts EU for European dealer warehouse search.
When faced with hard to find, nearly out of stock parts (for a 25 year old Camry model only sold for 2 years in the US), I had to go to extreme lengths to find some unique components. But after some searching of these places eventually found everything that I needed. Some required going back and searching again, a few months later (because parts sometimes do show up). Megazip was my hero on more than one occasion, finding an extremely rare part in a warehouse in Emirates in one case! The shipping was not bad, as these places specialize in global shipping.
Norm