copy monitor uses the UNIQUE IDENTIFIER assosciated to the element you are copying.
(You can find this Under "element id" in the properties of each element)
You can also locate that element in the model by typing the number into the "find by element id" button in the manage tab. Its a little green button off to the far right of the manage tab.

This means you can NOT copy/monitor it multiple times. This is done on purpose. If you want multiple instances of the same wing you need to use a different method than you currently have, because Revit will block you at the element id number if you try to have multiple instances of the same element.

Some of the other guys that do more production work in architecture will be able to tell you better workflows to use the same wing configuration in multiple orientations.

Thanks Karalon. Very good explanation

Would that hold true if I changed the mapping behavior from 'copy original' to 'specify type mapping'?

No, not as I understand this function.

This simply replaces all families of a certain type (example - "generic troffer lights") and will replace them with a new family type of your choosing from your Library (example - "2x4 parabolic troffer lights")

So when you copy/monitor that element it will replace it (in your model, not in the linked model) with the specified replacement type.

This is type mapping - ie mapping one type to another type upon copy.

But this does not solve the problem of the unique identifier "duplicates" which are impossible to create.

Gotcha.

Yes, Hopefully there are people here who have dealt with this same situation and have suggestions on how to handle identical part plans as you said.

In the meantime, I ended up copy/monitoring one whole wing and then stopped monitoring (just to get the correct air device model, location, and airflow) and then went to the next wing and did the same. I lose the ability to monitor changes, but its a viable workaround for now.

you could try making that room a group (once copy/monitored) and then copying the group to the identical room placements.