It is possible that we do have a match. Here is some additional information that I have on Albert:
Illinois: Roster of Officers and Enlisted Men APPLEGATE, Albert Residence Franklin, Illinois On 24 May 1861 he enlisted and was mustered into Company G, 16th Illinois Infantry as a Private. He reenlisted on 23 Dec 1863 and was mustered out on 8 Jul 1865.
US Military Pension Index APPLEGATE, Albert Henry, no widow listed, served Co. G, 16th IL INF, applied for pension on 28 Mar 1893 from CA, application no. 1101519, certificate no. 1008833.
California State Death Index APPLEGATE, Albert, age 74, died 1 Jul 1916, Santa Clara Co., State File No. 23959, no spouse listed.