Symmetrical was the term that my mind was seeking.
That is the aspect of the cover that requires evaluation. It appears that each component has a distinct part number for LHD or RHD, which implies that the overall part has a specific design for each location. However, if the cover is symmetrical, it could likely be exchanged.
It would be comparable to the exterior side mirror housings as opposed to the mirror glass. The mirror housings are different for LHD vs RHD, as they are not symmetrical and are angled and positioned specifically for the driver's point of view. However, the mirror glass (mounted inside the housing) is symmetrical, allowing for the use of any combination of plain, convex, or aspherical mirror glass in an LHD or RHD vehicle.