I am about to apply stucco with elastrometric coating to one side of a wooden exterior trash can enclosure. I have used exterior grade plywood. I am in the Southwest where there is low humidity year round and little rain, but when it does rain, everything gets thoroughly wet, but dries quite quickly due to low humidity.

I understand that a moisture barrier, such as roofing tar paper, is used as the first layer on residential walls.

None of my enclosure walls are in contact with the residence. Should I still use a moisture barrier where the opposite side of these "stand-alone" and stucco walls are open to the air? How about moisture weep space and bottom openings? Would they also still be needed?