This miniature portrait is signed "Otto Eckardt Dresden 1899" for the German artist Otto Eckardt, but it is part of a family trio of portraits, the other two being the adjacent portraits by Harriet Hutchinson Horton of his father John Houston Garth and his sister Anna Garth Goodlett.
Otto Eckardt worked in Dresden, Germany but he painted a number of portraits of American sitters. It is probable that a photograph was sent to him to copy, although another possibility is that Helen, John's mother took a photo to Europe to be copied around 1899, as there are records of her travelling to Europe around 1913/14 and she may have been there on a previous occasion.
The rear of the case is engraved "John David Garth - June 2nd 1874 - Aug 12th 1895", thus it appears it is a mourning portrait to commemorate his life.
Also shown here is a post card of the John Garth Memorial Library in Hannibal, Missouri which was completed in 1902. It was a memorial to his father John Houston Garth, but perhaps also to John David Garth as well, see about the library.
The library has recently been restored and photos of the restoration can be seen at River City Restorations, Inc. Hannibal, MO: Garth Memorial Library 951c