The word gringo first appeared in print in 1849 in J. W. Audubon's "Western Journal." J. W. assisted John James Audubon in the preparation of the plates for his "Birds of America" and other works and is well-known for his "Illustrated Notes of an Expedition Through Mexico and California, 1852. He reported in his 1849 Journal that "We were hooted and shouted at as we passes through, and called 'gringoes'."
There is no evidence for any association with "Green Grow the Rushes" and no clear evidence of a relationship to the San Patricios.