It’s a bilious looking concoction made from a sausage base. It’s made from cooked breakfast sausage, butter, flour, and milk. MILK.

I guess one could compare it to a bechamel if one were feeling generous.

https://selfproclaimedfoodie.com/country-sausage-gravy/

Red-eye gravy is another aberrant gravy from the US south. Never tried it, but I’m sure there’s some reason it exists.