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And then tap on the countdown clock repeatedly (5 or so times) and it will jump from ~2 minutes to a few seconds remaining, so the update will start immediately.
Of course it was. That's why the updates default to installing during the middle of the night. No matter how many times and how many ways people are told you can't use the car while its updating some people are still surprised at this-- like the clueless owner who thought he'd update while supercharging. You don't try to use your computer or smartphone while the operating system is updating, do you?
IME it also pauses charging during that time, so I set upgrades to install at, say, 10:30 PM so that my (scheduled, off-peak) charging begins at 1AM, as normal, rather than me waking up to find that the car had an hour or two less charge than normal