Sprinkler Required in Recessed Closet with Door?

I've come across several retail projects where there will be a "closet" that is just solid shelves about 18-24 inches deep and about four or five shelves tall, with a mirror across the front that acts as a door. It's certainly possible to provide a sprinkler outside of the closet and protect to the back of the hazard, but is this approach allowed?

To me it doesn't seem practical to provide a sprinkler at the top inside this shallow unit just as we wouldn't provide a sprinkler within the inside of cabinetry. If anything, the multiple solid shelves could prevent heat from collecting at the top and water from effectively reaching the bottom, although the door could also prevent discharge from reaching the bottom. Curious how others would approach these situations.

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