John used this pedal briefly around late 2004 or early 2005. Its purpose on his pedalboard remains unclear, as he was known to use his Ibanez WH-10 Wah almost exclusively throughout his time with the Red Hot Chili Peppers.
One possible explanation is that John added the 535Q Cry Baby as a backup in case his vintage WH-10 encountered issues, especially toward the end of the By the Way tour. Given the rarity and fragility of the WH-10, it would make sense for him to have a more readily available alternative on hand.
He used this on the song, ‘She Looks to Me’ during the solo. You can listen to it, and hear that the tone of the wah is quite different from his WH10 wah.