I just grabbed a reservation for November 21, since there's some available right now. I've been trying to book for Sept and Oct several times per day and haven't had any luck. I was going to attempt a walk up the other day, but snagged a Lamplight reservation instead.
I visited whatever it was called before the shut down in Feb. 2020 and did a walk up reservation. They took my name and said they would text me when it was ready and that it would be about an hour. We were starving and got some food from the Mexican place and got our text 10 minutes later (10minutes after they said one hour) saying our reservation was ready. We had to rush back over and we were technically "too late" but they sat us anyway. So, if you do get on a walk up list, you may not want to rely on whatever they think the call back time will be. If you venture off too far and they call you much earlier than what they said, you could miss out.