The calloutDidClickAccessoryButton is invoked by the framework when the user taps on the button in the callout. This is an indication that the user wants to see more details than available in the callout (which is space constrained).
Why do you want to invoke that method? You would typically only react to it being invoked.
Most often, you would place graphics (AGSGraphic objects) in a graphics layer (AGSGraphicsLayer) that was added to the map. Graphics can have attributes that would be shown in the callout when a user taps on a graphic.
I was able to test the AGSCallout class & AGSCalloutDelegate delegate completely once I figured out that AGSMapView has a AGSCallout property. Attached is a modified version of the GraphicsDemo.
See Lines 141-184 & 272-296 in GraphicsDemoViewController.m.
