More info regarding this find from another relic hunter :
From your photo of the mouthpiece on the yardstick. Your mouthpiece is from an "Eb Alto Horn" or a "Tenor Horn". I would say and Alto Horn. Your's is definitely from the Civil War by the thickness of the stem. Alto Horns are only used now in British Brass Bands, they have been replaced by the "French Horn" in the US and other countries. Alto Horns were used in every brass band during the Civil War playing the musical part between the Bb Cornet and the Bb Tenor Horn. It was Stephen Fosters favorite instrument and he wrote many great parts and solos for it. He called it a Peck Horn because of the emphasized off beat musical part that sounded like a Chicken Pecking. I'm not saying your mouthpiece wasn't used ina Bugle but the size would lower the pitch from the normal "C" or "Bb" to a lower pitch where it could not play in tune with other bugles. You've got a great piece but it must have been hit by a plow from the way the rim looks. It takes a lot of force to do that to a mouthpiece. Hope this helps!
In addition, a book i researched placed the 24th Iowa Regimental Musicians, XIII Army Corps, near the area where i dug this as they were in a funeral march for deceased 18 year old PVT Charlie Williams on Monday Nov 2nd, 1863.