Dear Ms. Osborn,
Thank you for posting your request on History Hub!
We searched the National Parks Service’s Civil War Soldiers and Sailors System and located a listing for a Frederick Domke who served in the 1st Regiment, Missouri Light Artillery. A search for Frederick Tompelkins does not turn up with any results.
We also searched the National Archives Catalog and located the records series Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the American Civil War in the Records of the Adjutant General's Office, 1762 - 1917 (Record Group 94) that includes a digitized file for [Missouri] Domke, Frederick - Age 20, Year: 1865 - First Light Artillery. Please note that not all Civil War service records have been made available online yet and there may have been more than one soldier with the same name.
If this is not the record you are searching for, please review NARA’s Requesting Copies of Older Military Service Records for information about how to request a further search of the records. This also provides information about how to request a search for a pension file for him. If he or his surviving dependents applied for a pension, the file may contain more information about his service during the war such as any disabilities suffered as a result of his service. For more information about conducting Civil War research, please see NARA’s Civil War Records: Basic Research Sources.
We hope this is helpful. Best of luck with your family research!