What about a recessed can just outside the closet? With a gimbal or eyeball trim, if you really want a lot of light in there..
I had no light in my hallway. I was considering putting a light in the linen closet that's in that hall, but once I put a can outside the closet (just regular reflective trim) it was plenty bright.
Otherwise, an LED strip light does seem like a good application here, going down the inside of the door jam if the shelves are tight front to back. Though I'm not sure what the NEC says about it, if you get a low-voltage fixture and put the transformer in the attic, I don't see that it would be prohibited.
I had no light in my hallway. I was considering putting a light in the linen closet that's in that hall, but once I put a can outside the closet (just regular reflective trim) it was plenty bright.
Otherwise, an LED strip light does seem like a good application here, going down the inside of the door jam if the shelves are tight front to back. Though I'm not sure what the NEC says about it, if you get a low-voltage fixture and put the transformer in the attic, I don't see that it would be prohibited.