From: Tony Oz
Date: 2020 Feb 17, 13:24 -0800
I mean to say - sighting two stars is NOT like sounding two lighthouses.
Both lighthouses are ALWAYS on the horizon, whereas a pair of stars can be seen as a non-horizontal plane (3 points with an observer included). When we build the equal-angle-separation LoP we are restricted to the horizontal plane of the piece of the "flat Earth". This is not so when we observe stars - the Earth is "geoidal".
My conclusion - the third LoP does not exist (at least - it is not azimuth-related).