hey Tim i don't see the exact backmark either but it can't be any older than 1902 , thats when the great seal button was first introduced as the official Army button . your smaller button is indeed a cuff sized one and the info about the design on the great seal is this ...
The design on the obverse (or front) of the seal is the coat of arms of the United States. The shield, though sometimes drawn incorrectly, has two main differences from the American :usaflag:. First, it has no stars on the blue chief (though other arms based on it do: the chief of the arms of the United States Senate may show 13 or 50, and the shield of the 9/11 Commission has, sometimes, 50 mullets on the chief). Second, unlike the American :usaflag:, the outermost stripes are white, not red; so as not to violate the heraldic rule of tincture.
The supporter of the shield is a bald eagle with its wings outstretched (or displayed, in heraldic terms). From the eagle's perspective, it holds a bundle of 13 arrows in its left talon, (referring to the 13 original states), and an olive branch in its right talon, together symbolizing that the United States of America has a strong desire for peace, but will always be ready for war. (see Olive Branch Petition). Although not specified by law, the olive branch is usually depicted with 13 leaves and 13 olives, again representing the 13 original states. The eagle has its head turned towards the olive branch, said to symbolize a preference for peace. In its beak, the eagle clutches a scroll with the motto E pluribus unum (":daydream:ut of Many, One). Over its head there appears a glory with 13 mullets (stars) on a blue field. In the current (and several previous) dies of the great seal, the 13 stars above the eagle are arranged in rows of 1-4-3-4-1, forming a six-pointed star.
hope this helps