Hopefully not going to piss anyone off here, but there is strange information in this thread.
The fact you have no paint color means you have a special paint color. Special paints were offered during the 1960s and there was a special paint book prospective buyers and dealers could use to order the color of their choice. There was an additional fee.
I am not sure where you found the number of "four cars"?? The truth is Ford recorded the fact your car was a special paint color, but they did not record the specific code or shade in their records. There were literally thousands of special paint cars and there are no records to say how many were any specific shade.
Paint manufacturers made colors available to all car companies. Theoretically Ford and GM could have the same paint color with a totally different name. Ford even changed the names on a yearly basis in some cases. One example is Poppy Red, it would become a special paint color (denoted WT5185) and later Calypso Coral. Sometimes dealers even gave special paint colors their own names. The Mercury line also had unique names for the same colors. Cougars and Mustangs were painted with the same paint and the names were very different.
Matching your paint is a good idea. The problem with that is you are going to get the closest modern version of the paint formula in the computer. Its is unlikely 1960s colors are even recognized today. Over the last 60 years paint formulas have changed for various reasons. This is why matching the paint has become a challenge.
I doubt you can not get the color name from any service or Ford. If you are really lucky you might find the original owner or the original dealer and determine if it was some type of special order or promotion. If you're lucky enough to find a build sheet it should have some codes on it.
I would also add a weird color does not mean the car is more valuable in my opinion, its just different
http://www.thecoralsnake.com/SPECIALS.html