Like Mrs. Lankford, I too have run across the term a number of times in regard to wartime Arkansans, as well as Missourians, who were thieving and killing during the war (do a word search of the O.R., using the terms jayhawk, jayhawking, jayhawker--you get Kansans, but you also get some other revealing tidbits). And, like Mrs. Lankford, my running across the term jayhawk in regard to individuals who sometimes clearly had no association with Kansans, or even regular or rogue Union troops or supporters, was at first very confusing--until I figured out that the reports were speaking of neither Kansans or Unionists. The term was being used as slang in regard to thieves and cut throats of no political persuasion, which led me to believe that it was in much broader use than we in the modern era realize. In essence, an already existing general pre-war slang term jayhawker (small "j") appears to have been applied to Kansans who were jayhawking, and they embraced it--evolving the term from the common noun 'jayhawker,' to the proper noun 'Jayhawker,' (as applied to them). The embracing of a term by some individuals that others considered derogatory is certainly not unheard of, as is indicated by Confederate guerrilla Sam Hildebrand proudly embracing the term bushwhacker (I imagine a quick survey could come up with dozens of other such examples).

As for "first discussion" of the term Jayhawker/jayhawker, I would be cautious in considering any "first" (if it is that) to be the authority on a matter. It certainly isn't in our own era.

Heavily-researched sources by writers who lived in the earlier era, and were either first-hand participants in Kansas events, or had access to the participants, indicate the term was in use in Texas and perhaps along the Platte River prior to the Border War, as well as by California 49ers in the Gold Rush. One such source even touches upon the Devlin discussion indicated in the first post of this thread. For research starting points, see--

William Elsey Connelly, "The Life of Preston B. Plumb" Chicago: Brown & Howell, 1913, p. 153
Simeon M. Fox, "The Story of the Seventh Kansas," Transactions of the Kansas State Historical Society 8 (1904): 13-49
Leverett Wilson Spring, "Kansas, The Prelude to the War for the Union" New York: Boston Houghton, Mifflin and Company, 1896