Scott, I found a couple of references to the Third Indian Home Guard, on Wikipedia, the Kansas State Historical Society's page, and on a couple of family search forums...used Google. This is what most had to say:

"3rd Regiment, Indian Home Guard
The Third Regiment was formed at Talequah and Park Hill in July 1862. It was commanded by Colonel William A. Phillips. Many of its troops had previously fought for the Confederate Army, particularly the First Cherokee Mounted Rifles that had been commanded by Colonel John Drew."

This was on Wikipedia and the Kansas Historical page. A couple of other places mentioned that the Third participated in the Battle of Old Fort Wayne, in the repulse of Watie's attack on the wagon train at First Cabin Creek and at Honey Springs.
One source said the Third was formed at Carthage, Missouri, but to me, Talequah and Park Hill seem more likely.