I don't know where it determines how long before it plays the blink animation, but this is where the animation is selected.
C0/A23D: B98016 LDA $1680,Y
C0/A240: C921 CMP #$21
C0/A242: F00F BEQ $A253
C0/A244: A921 LDA #$21
C0/A246: 998016 STA $1680,Y
C0/A249: A900 LDA #$00
C0/A24B: 998116 STA $1681,Y
C0/A24E: A900 LDA #$00
C0/A250: 990116 STA $1601,Y
C0/A253: 60 RTS
I don't think there's any difference in which animation will play between player characters. If there's an issue, maybe there's something wrong with human Glenn's animation data, causing it to pick inappropriate animation frames, or the frames it calls haven't been set up.