I can tell you this about AK… during his playing days he always took time to sign for fans before every home game. He and David Eckstein would each have a line of fans waiting for them specifically and signed without fail.
Outside of that, I have no idea what he’s like.
I think most players (not all) take some time to sign, just not all the time. I cannot imagine players making time to sign every single time someone asks or waits for a signature.
Maybe you caught him when he had some place to go. Who knows?
AK was great at spring training. Timing is everything.