The light on the ball is going to change daily from sunrise through to sunset, so if it is meant to match the moon then the same should be true of it.
Yes, the angle of the sunlight on the Moon, as seen from Earth, will vary, but the phase of the moon will not noticeably change.
Do this at any time you can see the sun and the moon, and the light on the ball matches the light on the moon. I've done this personally, twice over the last three days. Quite a coincidence, for a non-illuminated superheated cylinder, wouldn't you say?
Doesn't it suggest to you that the ball and the moon are being illuminated by the same light source?
No, you haven't done that, this whole line of inquiry is ludicrous. The moon does not magically change from having its left side lit to having its right side lit over the course of a day, while that would obviously happen with a ball lit by the Sun. Are you kidding me?! Seriously, what the actual thork are you talking about?
I don't think you are getting it.
1: Use any day where the sun shines and the moon is visible.
2: Hold a small ball in front of you in the direction of the moon (so that it is just in front or besides the moon for comparison)
3: Observe
Result: The small ball is exactly lit just like the moon, showing the same pattern of shadow as the moon.
I've done this myself aswell, and it ALWAYS shows this result.
If we use this observation, and construct an explanation that the moon is lit by the sun, it makes perfect sense.
If we then apply this explanation to all observations of the moon, we can easily conclude that the sun goes below the horizon and below the ground we stand on, especially on a full moon, where it should be opposite the direction of the moon.
It also explains why there is never a full moon when the sun is up and why the new moon is only present when the sun is up.
Everything points to a globe with these observations, but as all FEers, you will either reject the observations, try to make some weird magical FE logic for the observation, or ignore it completely.