I have using a white piebald cockatrice for a quest: "University is looking for a Piebald Cockatrice to demonstrate on the genetics lecture."  His dominate "piebald" gene has been researched, but he's not showing up as an option for the quest.

But the resulting color is white, not piebald.

They are looking for a cockatrice that has piebald appearence, not for the one who has dominant piebald gene.

Please note that the quests aren't random, all of them have some kind of small backstory or logic. The University wants piebald cockatrice to show the students how the piebald gene suppresses the production of pigments. But the appearance of a white cockatrice who have piebald gene doesn't differ from the one who hasn't. There's nothing to suppress because of the other gene that has systemic suppression of the pigments, and nothing to demonstrate for this lecture.