I happened to have a copy of the Rav Soloveitchik Yom Kippur machzor, which alluded to the story (from Rabbi Rakefet's book) about the Rav and his father at sunset on Yom Kippur. Reading the story made me wonder: how in the world did they have time for a break between Minchah and Neilah? If the sun had already begun sinking below the trees turning the sky all kinds of nice colors, wasn't it time for them to start davening already.
We always rush right from minchah onto Neilah. Did they daven differently? Did they fast later than everyone else where they lived? What gives?