Lunar Terminator Paradox

There's an optical illusion known by names like the "lunar terminator paradox". This has much discussion and descriptions online, but none made sense in my head, so I wrote this program to figure out what was going on. The paradox:

I was camping in the mountains with a friend recently. We were looking up at the sky, just after the sun has set. The moon was clearly pointing up.

After playing with this program , I have clarity: we're looking up at the moon from below. The most pathological case is a full moon. Let's say the moon is on the horizon: elevation=0. If we're looking at this low moon, and the moon is full, the sun is directly behind us. The moon is fully illuminated, and we see 100% of the moon disc lit up.