Given the historical comment that "Lt. Baker" was from Knoxville, Mo., I'm wondering if this isn't our guy--

https://www.familysearch.org/ark:/61903/1:1:MHZM-4LM

If it is, the linked family tree indicates he's James Carson Baker, this guy--

https://www.findagrave.com/memorial/147106787/james-carson-baker

Which maybe is this 2nd Lt. in Company G, 6th MSM Cavalry (age on card is off, but rank, middle initial and geographic setting matches, and he's discharged in plenty of time to be established in the Ray County area militias and participate in the ambush of Anderson)--

https://www.sos.mo.gov/Images/Archives/Military/s00840/s00840_0211.pdf

Maybe pension file and data on him would shed some light....