Charles---Stephen Hinks' MA thesis (William and Mary 1988) "A structural and
functional analysis of 18th century buttons"  states generally that "toward
the end of the 18th c. the stamping of back marks on buttons began"
referencing Hughes and Lester 1981 "The Big Book of Buttons."  This fits in
well with technological advances in metal working and particularly in
electroplating (tinning, silvering and gilting) after the 1740's. Calver and
Bolton in "History Written with Pick and Shovel" (p.146) state: "The practice
of stamping names and marks of quality upon buttons did not obtain in the
18th c., but immediately at the beginning of the 19th c. English button
makers began to stamp upon the backs of their products  the name and place of
business of their respective firms."  That is about as specific as anything
I've found.   Good Luck, and keep us posted if you find anything better. Carl
Steen