Atlas pistols have a secondary firing mode that allows them to use one of several types of tracking rounds that can be used to tag enemies. Once tagged, all normal rounds will track the tagged enemies for an amount of time that is dependent on what kind of tracking device was fired.
The AX-19 has neither the rate of fire of the AX-7, nor the splash damage output of the AX-88, instead being fully automatic with an average rate of fire. However, any character skills, class mods, or relics that increase weapon fire rate, especially Atlas weapon fire rate, can make very effective use of an AX-19, doubly so when using its alternate fire mode to track targets.
The AX-19 is obtained randomly from any suitable loot source.