The obscure part is what the original intention for Mercury was. Apparently, it would share a body with Lincoln, rather than the case from the 1941 models onward where Mercury shared bodies with Ford.
Here is this photo of a model where the design is close to the eventual 1949 Mercury below the belt line, but with a heavy, fastback greenhouse. Most likely, this dates after Breech ordered that Mercury get what had been the '49 Ford body. So far, I've found no photos of full-scale clay models of earlier Mercury design proposals from around 1946 or '47.
In this book, Paul Woudenberg suggested that the original intent was for Mercury to have the bustleback version of the large Lincoln body, and Lincoln was to have a fastback version. Somehow, this strikes me as being a questionable use of resources, given the postwar drift away from fastback acceptance in the marketplace. Knowledgeable readers are urged to clarify all this.
In the end, only Lincoln got the large body -- in both fastback and notchback varieties. This class of Lincolns was marketed as Lincoln Cosmopolitan. And then there was a line of just plain Lincolns. These were based on what was now the '49 Mercury body. About 48 percent of '49 Lincolns were Cosmopolitans, but I haven't found what share of Cosmos were fastbacks. Probably not a large percentage, because the fastback line was dropped for the 1950 model year.
Even though the numbers of '49 Lincolns and Cosmopolitans were almost the same, a glance at Google Images when searching on "1949 Lincoln" suggests that the majority of survivors in good condition are Cosmopolitans, including some fastbacks. Something to do with prestige and rarity, I suspect: fancy rare cars eventually become more treasured.