I believe we've seen this one before Andrew. I recall a similar discussion. I can't remember for certain, but I think the consensus was that these were U.S. Govt' cars.
Now that you mention this, I do recall Dad saying that a lot of Guv'mint cars were 2-door, for some odd reason. So now it makes a bit more sense, in that respect, but why are they parked like automotive sardines on a Chevron lot?
The Sinclair filling station in photo (below) in Springfield operated by Jim Culver opened 1951. The State Union-Register image was taken during the grand opening celebration of the facility. Courtesy of The Old Motor
Here is a 1960s view of a modern Clark Super 100 facility. Clark Super Gas was established in 1932, one of the most difficult years of the Great Depression when Emory T. Clark constructed a gasoline station for a customer in Milwaukee, Wisconsin, who was unable to pay him for his services. To recoup his investment Clark opened the station himself and in time built others and developed the enterprise into a very successful midwestern chain marketing only high test premium fuel. By the 1970s Clark Oil Corp. owned and operated close to fifteen-hundred filling stations and has survived until today. Learn more about Clark Oil’s history here. Courtesy of The Old Motor