Mystery solved! Not "atonal" at all, but At-tunal, which means "Water-Sun" in Nawat, the language of the Pipil, who are indigenous to El Salvador. It's supposedly the name of a Pipil prince who helped another Pipil, Atlacatl, repel an attempt in 1524 by Cortes henchman Pedro de Alvorado to bring present-day El Salvador under Spanish control. (Alvarado was successful a few years later.)
If you don't know Salvadoran history, the Quick Response Infantry units ("Atlacatl" was the first) were formed in the early 1980's to go after leftist guerillas. After plowing through all the human rights reports that mention the Atonal division, I'm glad to find the name has nothing to do with music.