The reason I said that Jack has a little bit of Tik-Tok in him is because the character of Tik-Tok was at one point the property of the king of Evin Baum's novels, which is mirrored in the show in terms of Princess Langwidere/Lady Ev making Jack her property.

I was also thinking of the character of Tik-Tok as he's portrayed in Return to Oz, where both he and Jack Pumpkinhead are directly associated with Mombi, who is a composite character written with characteristics from both Mombi and Princess Langwidere.