This is not a post about Eliphaz (rich though that subject may be), rather it's about Temanites. "Temanite" is a gentilic, coming from the root YMN: you add some vowels and a t-prefix (that's a fairly common thing in Hebrew), and you wind up with Teyman. Now, "YMN" means, "right hand." YMN also shows up in "Benjamin": it's, etymologically, "Ben-Yamin," "son of my right hand." So the Temanites were some folks who lived in the south (relative, of course, to the Hebrew speakers who dubbed them this), because the directions are given relative to the facing sun.
This right-hand/southpaw duality, of course, explains why Sandy Koufax pitched left and batted right.