John D. Brinker of near Warrensburg, Johnson County, did survive at least into November 1863.
As you say, Captain Quantrill did send Brinker to General Price with his report dated 2 November 1863 ("Official Records", series 1, vol. 53, pp. 907, 918).
The 1881 Johnson County history on page 690 states also that in 1867 William H.(?) Brinker and his older brother want west, drove cattle to Salt Lake, worked on the Union Pacific RR in Wyoming and moved back to Johnson County with their mother's family in 1869.
However, the Probate Records of Johnson County show the probate settlement of John D. Brinker in 1868 at the Johnson County courthouse contained large acreages in Township 45, Range 26.
The John Brinker of Quantrill fame was John D. Brinker, unless I am misinformed (age 19 in the 1860 MO Census of Johnson County, MO by that name). Therefore, I am inclined to believe that the Civil War guerrilla died sometime between late 1863 and 1868, and the William H. Brinker was perhaps another family member.
I see that John D. Brinker's sister Mattie went to Mexico postwar, so I wonder if John was one of the many Missouri Confederates who exiled themselves to Mexico at war's end.