Your 1964 Cooper S family car would be worth a "mint" over here now.
You are correct regarding the fuel tank as it was an option on the Cooper S models only and became standard fitment from January 1966.
I had enough trouble with my one tank when I had to change the left rear shock and all the tank fittings and straps were rusted etc !
The sender has never been accurate since, so the old marked bamboo stick is a most important tool. I don't leave home without it.

( Ken Hyndman )