I found a copy of Andrew Elders military records in a box of old papers. He enlisted in the U. S. Army on April 27, 1898. He listed William Davis (Alma's eldest brother) of Braymer, Missouri as parent or guardian in his military records.
He is definitely tied to Alma Davis, Drew/Drury Elder's (1808 - 1881) second wife, but was born before their marriage.
Lots of room for speculation.
Interesting aside: He was three days AWOL 24 - 27 Aug 1898. Fined $5.00 and sentenced to 10 Days in guard house