Great tip from James Herndon:
The secret lies in the original array line itself, that line, the one that shows up next to the array and lets you change the number of objects inside of the array, is actually an element in and of itself, and you need to select it too before you perform the mirror or copy function.
Now you can see that after I’ve mirrored the array the new array has an array object associated with it and will let me change the array after the fact.
The Revit Blog: Arrays – Part II
Interestingly, you can select the Array line and add it to a Group. You can also use the IDs of Selection tool to get the Element ID of the array itself: