Your 2-piece brass button with "G.G." on its front is shown as button #CO-4 in the American Uniform buttons identification book by Alphaeus H. Albert. The "G.G." stands for the Governor's Guard of Colorado. Your profile shows you live in Colorado, so I looked for that state's buttons in the Albert book. Colorado became a state in 1876, so I would guess your button dates from sometime between the 1880s and the early 1900s. Knowing what the backmark says would help narrow down that time-range. Please clean the backmark a bit more. I think it says "DEVLIN & CO. N.Y." and if I'm correct your button would be from no later than 1893, the year that Devlin & Co. went out of business.