Found a Pension Index card for a James Baker, wife Esther; Co D and H, 1st Mo Engineers and Co F, 25th MO Infantry. This would connect him to Pvt Charles Morton and Centralia.
FWIW

https://www.ancestry.com/sharing/11385565?mark=7b22746f6b656e223a225236396f57664c4359334b4c674a42424b6b314b61362f31624b4e67492b686d4b653170794a4e46487a513d222c22746f6b656e5f76657273696f6e223a225632227d