Faldage, I'd bet money that you're right. My uncle--in Tennessee! (welcome aBoard, Johnnie)--used to call "gee" and "haw" to his pair of plowing mules (George and Henry) to get them to turn right or left. And any time there is more than one animal, they need to turn (work) together.
Hmm--it just occurred to me that this is yet another ex. of the anti-sinister world: I have only heard the words as gee and haw; never haw and gee.