In case this is useful to anyone else:

I certainly can't ascertain any rhyme or reason to the walgreens website. Yesterday at 10:30 am I logged on and there were tons of available appointments for today, including at numerous locations that hadn't yet shown availability.

And my mom got jabbed this morning. It takes a lot to impress her and she said it was a very smooth process

So my advice is to keep at it.

Are new appointments posted at midnight? Some other time?

Thanks for any tips.