NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John D. Howard
Date: 2019 Dec 2, 17:53 -0800
Mike,
Short answer: No. The Longitude by Noon sight is something different.
If you search this NavList ( use TOOLS then Search ) subject " Time Sight " and change starting date to Jan 2002 you will get over 300 messages on the time sight. A good discussion was had around Nov and Dec, 2012.
Before about the second half of 1800s the Line of Position was not used. Navigators got Latitude from a noon sight ( maby Polaris ) and then Longitude from the time sight. The time sight would give you local apparent time - like a very accurate sundial. To get your longitude you would need the time at Greenwich either using a watch ( cronometer ) or by shooting a luner. ( The luner only gave you Greenwich time, the time sight gave you longitude. ) This is where the equation of time came into play. The watch gave Mean time, the time sight gave apparent time. The difference is EOT.
I am not an expert or a teacher so I urge you to read the many messages from the past. I would start with Frank Reed's message " A time sight Primer " from Dec 24, 2012.
John H.