The 386NL is handed because the hole for the cylinder body is not vertically centered in the escutcheon.
The 5/8" hole for the cylinder tailpiece itself always aligns with the exit device centerline and the trim escutcheon centerline. Since the cylinder tailpiece sits toward the bottom of the cylinder body, the center of the cylinder body hole sits above the centerline of the escutcheon. If you would flip the trim upside down, the center of the cylinder body would be below the centerline of the escutcheon. In this scenario, the cylinder would have to be mounted upside down in order for the tailpiece to align with the exit device. If the cylinder were mounted upside down, the keyway would also be upside down.
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