Not a major battle, but it has the distinction of being the westernmost one of the Civil War, I think. The rebel troops were commanded by Jack Swilling (later founder of Phoenix), and if my memory serves me right he was captured. But after Hunter abandoned Tucson, Swilling ended up at Pinos Altos for a while, then accompanied the Joseph Reddeford Walker party back into AZ in March or April of '63, maybe? He wasn't one of the 12 members of the Hunter force that made it back to Mesilla, in any case.
Swilling was the shaker and mover who lured Mangus Colorado into captivity, leading to his death at the hands of the California Column troops in March, '63. He's Jacob Snively's partner, on and off, throughout the latter years of Snively's life. Evidently Swilling was among those who gave Snively's corpse the initial burial a few days after he was killed by Apaches at Vulture Gulch in, what? '71?. 7 years later Swilling went back for Snively's body and reburied it at Gillette, Az. That project led to Swillings own death in prison, by a circuitous route. A whole story in and of itself.
Not that all that tells much more about the battle you asked about. Fact is I've never found much documentation about the battle, though I'll like to read the military reports. I'd guess they're probably stored in California... the battle took place before the Column arrived on the Rio Grande. The military correspondence after that time ended up in the US Archives, but prior to Carlton's assuming command in NM the correspondence went back to CA, thinks I, and is probably stored in the CA State Archives.