A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Fleming
Date: 2018 Jul 8, 13:18 -0700
Either I missed your point or I think you missed Frank's point.
You said with the Sun near zenith ...,
I thought you meant on a day where the meridian transit would pass overhead. Is that what you meant to say?
On such a day, The altitude above east or west horizon will change at 15 degrees/hr, all day long.
There is no extended time period when the altitude doesn't change with time.
Frank's hypothetical is trying to get a meridian transit sight, ex meridian, by using north or south horizon and letting the altitude error for non vertical altitude produce the added ex meridian altitude.