Well, Faquarl has his vanity but it's different compared to Bartimaeus. He doesn't exactly go for aesthetic beauty like Bartimaeus does. Faquarl's approach can be summed up basically to "I'm trying to look like I don't care how I look." His human forms compared to Bart's tend to be more down to earth, more homely. I'd say they're more practical for his purposes too.
That's why for his chef form I went for a stockier build, hairy arms, thick eyebrows, etcetera.
When trying to figure out his hair, I tried experimenting with clips, because whenever I have to put my hair up like that I usually at least need one clip for my hairs that are too short to be tied back. It would be practical; I only figured out it looked kinda cute afterwards as an unintended side effect. I am weak so I kept it instead of changing his hair style.
...I should draw him with different hair clips in the future; there would probably be some humor to be found there.