But the John Anderson in northwest Benton County served in a Company D, and if the gravestone reads Company A, the other John Anderson might be one you seek, as he lived in southern Benton County, and some with Union sympathies from that area enlisted in the Hickory County Battalion of Osage County Home Guards. His service card shows he served in Company A, and enlisted in Benton County:

http://www.sos.mo.gov/TIF2PDFConsumer/DispPDF.aspx?fTiff=/archives/AdjutantGeneral/Civil_War/ServiceCards/s883/1800.tif&Fln=S38268.pdf

Here is a brief description of that unit:

Osage County Regiment and Hickory County Battalion Home Guard Infantry
Organized by authority of Gen. Fremont June and July, 1861. Duty in Camden, Miller, Hickory, Benton and Cole Counties, and at Jefferson City until December. Disbanded December, 1861.