The technical name for that little stopper pin is a "pintle."
Stopper #1 - 1938 to Early 1950s
Stopper #1 appears on the original pottery bottles, and on the earliest glass bottles starting in 1946. The bottle is capped with a tin shroud on a cork which is pressed into the bottle and sealed around the neck. The pintle is tin with a top disc nearly 5/8 inches in diameter. The top disc comes to a small point in the middle. Note the wide collar at the top of the stem (left photo). This wider collar has a recess into which the small rim on the bottle top fits to secure a seal.
Stopper #2 - Early 1950s to 1956
Stopper #2 appears on the glass bottles in the early 1950s. It is similar in shape to Stopper #1 but is only 1/2 inch in diameter. The tin shroud is attached to a polyethylene stopper that proved more effective in sealing and resisting the effects of alcohol. The pintle is a pinkish polypropylene and still has the little bump on the top.
Stopper #3 - 1956 to 1970
Stopper #3 shows up in the mid 1950s and is gray polypropylene. The top is eight-sided, measuring 19/32 inches across the flat sides and 1/8 inch thick. The pintle has a round disc on the top with no discernible bump. By the 1950s the shroud around the bottle top is aluminum. When viewed from the side, there is a slight curve from the stem to the top.
Stopper #4 - 1970 to 1993 (present day)
Stopper #4 differs from Stopper #3 in several aspects. There is a star molded into the top disc of the pintle. The top of the stopper is thicker at 3/16 inch. When viewed from the side, the stopper is a "T" shape with no curved shoulder.
Stopper #5 - 1967 to 1970
Stopper #5 is identical to Stopper #3 but in white rather than gray polypropylene. The white stoppers were introduced on the new "alternative fragrances" introduced in the late 1960s: Lime and Burley.
Stopper #6 - 1970 to 1993 (present day)
Mirroring the evolution from Stopper #3 to Stopper #4, Stopper #6 is similar to Stopper #5, but white with a thicker top and square shoulders. It continued to be used on Lime, Burley and Leather traditional bottles.