I don't think its authentic. The "G" seems uncharacteristically large in height when compared to the K. if you look at his signatures, the vast majority of them have both letters at approximately the same height.
All my Gibson signatures have been since he has been with the DBacks so not sure how he signed in the late 80's. Most of mine were in a good setting with him sitting in the Dugout or standing at the dugout rail. Every single one of the 12 Gibson signatures I have he connects the G to the i.