MackDog, thanks for confirming that your US Great Seal button is the small-size version. It should measure 16mm, not 14mm. If possible, please confirm that measurement.
As Duggap indicated, being the small-size with an iron/steel back means it was used on leather, because rust from the iron/steel back would make a stain on cloth. So, I believe its most likely that your button is from the leather hat-strap on a US Army "visor" cap. See the photos below, showing examples of "visored" US Army caps from the World War One and World War Two eras.
Narrowing down the time-range of your button:
"Great Seal" US Army buttons were first issued in 1902, and are still in use today. The 1902-to-1910 version did not have a raised rim, so yours is not that version. The version manufactured from approximately 1910 to 1923 had a raised rim and "black finish" (which is not black paint) on the button's brass front, as a form of camouflage. In 1923, the black-finish was discontinued. Your somewhat corroded button seems to have a few small remnants of "black finish" on it. Please confirm whether or not that's what I'm seeing, or if it is just black-ish crud on the button. If it's actually remnants of "black finish" your button, it dates from 1910-1923. Otherwise, your button is from later than 1923.
I'll include a photo showing a group of non-excavated ("non-dug") 1910-1923 Great Seal US Army buttons, showing the "black finish" on their brass front. Remember, it is not black paint, but instead is achieved by using a chemical process which blackens the brass.
One of the hat photos (below) shows a visored US Army Model-1902 cap whose maker's-label says it was manufactured in 1906, and you'll notice that the Great Seal button on its leather strap does not have a raised rim. The other photo shows a World War Two era cap, whose button has a raised rim and no "black finish."
