From the What is it? Forum
I did some research for you on your 24th US Cavalry Regiment tag-or-leather-decoration. (The stamped-sheetbrass dome with three "foldover" tabs on its rim, for attachment to thick leather or other material.) The 24th US Cav was a Buffalo Soldiers" cav regiment, meaning, its enlisted-men were African-Americans. It was reorganized into an Artillery unit in October 1917.
https://www.globalsecurity.org/milit...rmy/2-82fa.htm
"In October 1917, the 24th Cavalry was reorganized and reequipped as an artillery regiment and on 1 November 1917 redesignated as the 82nd Field Artillery Regiment."
Few modern Americans seem to know about the brief (March 1916 to 1919) US-Mexico War, in which the US Army invaded Mexico as a result of cross-border raids by Pancho Villa. At the order of US President Woodrow Wilson, US General John J. Pershing of World War One fame led his troops into Mexico in March 1916, finally withdrawing them a year later, March 1917. Some troops from the US 24th Cavalry got themselves captured, whom the Mexican Government used as a bargaining chip to get the US to withdraw from Mexican soil.
Down Mexico Way | Shot in the Dark
I suspect your 24th Cavalry tag/ornament, which you found in Arizona, a US-Mexico "border state," was lost there during the actions against Mexico. The December 1914 date-stamp on your .45-caliber bullets, combined with the October 1917 ending of the 24th Cavalry, establishes the time-frame of your finds.
Your .45-caliber cartridges marked FA 12 14 are for the newly-invented and now world-famous US Army Colt Model-1911 Automatic Pistol. I should mention, they were also used in the equally famous Thompson Submachine Gun, also known as the "Tommy Gun."
The large brass disc with a brass bar across its back is a US Army "Great Seal" rosette from a horse's bridle. It was first issued around 1904. You can see one in the photo below, which shows a US Model-1909 bit-&-bridle harness assembly.
I'll also include a photo showing the domed sheetbrass 3-tab leather accouterment/decorations, on a horse's "backband saddle."