The original SRI mouse (Engelbart, et al, mid-1960's) had one button.
By 1968, it had three buttons. Only the left button was used in
conjunction with pointing. The other two buttons were used to confirm
and cancel actions.
In 1974, at Xerox PARC, I implemented a prototype of the Gypsy text
editor that introduced drag-select and needed only one button. (The
final version of Gypsy, 1975, which I developed with Tim Mott, used
all three buttons because they were there.)
In 1981, Xerox shipped the Xerox Star with two buttons.
Apple's mouse first appeared on the Lisa.