The 1950 Mercury cars started out with the patent /ID plate on the right side of the cowl as shown and the body plate in the same location on the left side. The body plates were combined with the patent plates one above the other on the later 1950 Lincolns & Mercury cars. The body plate is what you need to find.
The 6-passenger coupe had three trim levels after the Monterey came out. The lowest trim level was the 72A and it was a basic model with fixed rear quarter windows. The 72B had rear quarter windows that hinge out for venting as well as a few other nicer trim applications. The 72C was the Monterey. It had all the characteristics of the 72B but the extra trim package such as the vinyl top, extra chrome trim, and the Monterey badges and markings. The wing on the hood ornament was gold instead of chrome. Those interior window garnish moldings were chrome as seen in the photos. The new wheel covers for 1951 had the polished brass Mercury head as standard on the wheel centers. These were optional over chrome on the lesser trim models. Leather seat coverings were also standard for Montereys but there were options on that and could have faux leather combined with real leather as well as all leather options. They had their own distinct color options from the lesser trim models. Some accessories were still optional even on the higher end types.
These were in unison with the Ford Crestliner, the Lincoln Lido, and the top of the line Lincoln Capri models.