Is it possible to have eczema down where the sun don't shine?

Yes, but not common: Eczema in the underwear area is not common because it has more humidity and isn't too dry. The area also doesn't get scratched as much. If there's eczema there, it's usually at the top of the butt crack.

Yes: It's possible to have eczema wherever you have skin.

Possible: Usually, where the sun does shine actually helps eczema.