Bman, I gave you a chance to be first this time. ;-) The button seems to be a Civilian-usage imitation of a US Army "Staff-rank" Officer's button. Staff-rank meaning, its use was limited by Regulations to the rank of Lt. Colonel or higher. That particular version was in service from 1832 to 1902, when it was replaced by the goldplated version of "US Great Seal" button. But as I said, this one seems to be a Civilian-usage imitation of the actual Military button. The Civilian-usage version dates from the early 20th-Century.
I had to Edit my original reply, because I discovered I'd missed seeing the photo of the button's front. After I examined that photo, and then re-checked the photos of its back, I now see that it looks like it does not have a separate rim, which an actual 3-piece button always has. It may be a 2-piece button which was deliberately manufactured to very closely resemble a 3-piece button. Collectors call thar type a "false 3-piece" button. One of those is shown on the right in the photo posted by BigCypressHunter.
Let me give public credit to BigCypressHunter for causing me to take a closer look at Deepseeker3's post.
Deepseeker3, I'll need to see well-focused closeup photos of the button's front. I can't see enough in the far-away photo of it to tell whether it has a separate rim/ring around the domed part. In the back-view photos, the whole thing seems to be just a single piece of brass. Compare your button with the one on the right in BCH's photo, which is a "false 3-piece" button, and the one on the left, which is an actual 3-piece button.