The sinking ship effect is actually a proof for a Flat Earth, since it has been found that a half sunken ship is a perspective effect which can be restored with the aid of a sufficiently powered telescope. There are many first hand accounts of this in the Flat Earth Literature linked in my signature.
The Lunar Eclipse is not a proof for a Round Earth because there is no evidence that the shadow which manifests upon the moon during a lunar eclipse originates from the earth at all. That shadow which appears on the moon could come from any celestial body intersecting the light between the sun and moon.
The shadow experiment works on a Flat Earth since the sun is close to the earth and its light is vertical overhead and horizontal at its setting. This will cast shadows of different lengths depending on the position of the sun. We can accurately calculate the sun's true distance of 3,000 miles above the surface of the earth through this method.