OK. I literally don't understand how you're not understanding this but here's a diagram which may help.
This is what the illusion looks like. Here's a photo of it:
And here's a diagram, this is actually very similar to how it appeared when I did the string experiment myself:
It looks like a line perpendicular to the terminator is pointing into the sky, the diagram shows the line pointing perpendicular to the terminator, that's where the light is coming from.
But the sun is setting so how can the sun be illuminating the moon? That line doesn't point at the sun. Or, if it is the sun illuminating the moon, the light must be bending.
In fact above in your "diagram" above you have made the "string" bend to make it point at the sun. And your string is not perpendicular to the terminator, that is important.
If you are holding a piece of string taut in front of you so it is straight and you line it up perpendicular to the terminator then it looks like it must point off into space.
But it you try it you'll find that it doesn't. It points at the sun. It doesn't look like it should, granted, but that's what illusion means.
That proves that the sun IS illuminating the moon and the light is NOT bending. The apparent mismatch is an illusion.
And, again, you keep ignoring this. If it is the light that is bending then it must be bending DOWN, not up as claimed by EA.