For the rest of the world; notice also how the width of the shadow varies according to latitude, just as expected on a globe; thinnest shadow at equatorial regions, wider the further you go North or South ...
The sun and moon are (in general respects) over the equator in the Flat Earth model. When you are casting shadows on parts that are further away, they tend to grow.
How does this show a Round Earth, specifically?
Reading this thread on eclipse prediction I think there is agreement on these two things:
1. The day of an eclipse *can* be predicted using Saros cycles.
2. Saros cycles do not predict the exact locations on earth where an eclipse will be seen, this requires complicated calculations.
Am I correct? Is there agreement on these two items?
The day and time of the eclipse can be predicted with the Saros Cycle.
At the end of the Lunar Eclipse chapter of Earth Not a Globe Rowbotham shows that similar pattern-based methods
can predict the time, magnitude and duration of the Lunar Eclipse (scroll to the bottom).
If you want to know whether the sun or moon will be seen in the sky at that time, so that you may be able to see it, you need another way of determining that; such as a solar or lunar clock or model.
With knowledge of the the Saros Cycle patterns, and the patterns of the sun and moon, it is possible to create such maps on where the Solar Eclipse may be seen. In the case of the Lunar Eclipse, the challenge is more trivial and applies to anyone who can see the moon.