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So I went to the software screen on my S. It said “up to date”.
Then, I pretended to press advanced a few times. The screen changed to “checking” and then to “ready to download”. I didn’t even have to touch the screen! Just the mental power worked!
You're right! I went to the software screen, it said "checking for updates", so I pretended to poke the advanced button. It took a bit longer than expected, maybe a few dozen almost-presses, but then the update started downloading!
In summary, it's going to the software tab, not pressing the advanced button, that prompts the check for updates.
I am not convinced of the validity of my own post either, but here is another anecdotal to further confuse things. Earlier the same day I had connected to the wifi at the Austin Tesla Service center and that too can supposedly initiate an update, which makes more sense than the button pushing, When I went to get my screen yellowing fix I got an update notice before the Uber arrived to pick me up.
If there is not an update available nothing will ever happen.