The reason why techniques from antiquity don't appear to match our understandings today is because today we are so much more precise in our measurements.
When an accurate navigation across the Atlantic Ocean meant you arrived within 500 miles of your destination and then navigated along the shoreline to reach your destination, using a sun compass was a very accurate means of navigation!
Back in the pre-GPS days, I used celestial navigation combined with pressure line of position techniques to navigate C-130's across the ocean. My standards were to be within 10 nautical miles of course and 5 minutes of time from my most recently passed ETA in the position report to the ADIZ entry point.
Today, if you achieved an accuracy better than half that with GPS pilots would be screaming bloody murder that their equipment was screwed up!
If you were in the Northern Hemisphere and created a sun compass, you would start with a white disc with a pin in the center. In the morning you would hold the compass vertically, with a consisten orientation of the disc, and measure the tip of the shadow formed on the disc.
Then, at various increments of time, you would keep this process going until you constructed the points as forming an arc over the disc from one side to the other. At the point where the arc reached its apex, this would be true north. If you were in the southern hemisphere, the point where the arc reached its apex would be true south.
Indeed, the point you first measured the shadow in the early morning would be approximately true west and in late afternoon would be true east. At least for mariners several hundred years or more ago, it was accurate enough to enable them to get within reasonable distance to their desired destination and back home again.
Using modern measurement standards, we can determine that it isn't all that accurate. But, I know of people who decided to sail boats hundreds of miles using just a sun compass and it worked just like it worked in antiquity.
And for those wondering, when I used celestial and pressure line I normally arrived at the ADIZ point (and associated radar coverage) within five miles and two minutes of time. That was pretty good back then!
Cheers,
Ken