I think the 3rd IHG is likely except that it is odd he is not on the any rosters that I can find. I don't doubt that the reference to "3rd Indian Infantry" means the 3rd Indian Home Guard, the "Pin Regiment". If he was white or mixed blood, perhaps he became a civilian contractor or was in a white unit attached to the 3rd IHG. The Pins were almost exclusively full bloods. I'm just speculating.
The Indian Home Guards were "mounted infantry" as opposed to "cavalry". The difficulty of keeping healthy horses resulted in more and more of them dismounted. In Phillips' report of his Feb 1864 expedition, he referred to them as his "infantry" but I'm not sure that meant they were not mounted. They were armed like infantry -- his cavalry had carbines. The Indian troops often provided their own Indian Ponies (13 hands tall give or take). The Cavalry wanted thoroughbreds that were 16 hands tall when they could get them. Wiley Britton said the soldiers of the IHG looked comical because their horses were so short.
Was Sarah Wofford his spouse? I found a reference to a pension application that she apparently submitted. "Wofford" may be her name from a subsequent marriage.