Sorry, should have thougth out a reply better before writing that up. In response to your commens on the evolution of ther term, here is my take:
1. Prior to Kansas Troubles, the term existed, the meaning probably varied plece to place, in general the term is relatively obscure.
2. Pat Devlin incident and McReynolds May 1858 newspaper article introduces word into the vernacular of the Kansas troubles, verb (jayhawk) and noun (Jayhawkers) emerge almost simultaneously, and along the MO-KS border the word quickly comes to signifify men affiliated with the Free State cause like Jennison, Snyder, Brown and the outright criminals that often ran with them.
3. Jayhawk meaning to signify "steal or rob" grows at the same time.
4. Creation of Seventh Cavalry extends Jayhawker meaning to specific Kansas troops, then Lanes jayhawking expedition extends the meaning more generally to all Kansas troops. At the same time, the term continuess to be applied to outright criminals.
5. Term varies with geography - see previous examples of Arakansas and Louisianna.
6. Term varies with time. By 1877 , as inidcated in Bartlett's dicitonary, the dominant meanings come to be lawless soldier, freebooting armed man, and guerilla - except in Kansas where it denotes the brave men of the State who saved Kansas for the Free State cause and later the Union.