I have always enjoyed playing with incognito characters when I write. There is something so liberating about a mask. It lets your inner self sneak past the presuppositions of others and make itself heard.
What does your character have to say that he or she can say best from this advantage? Suppose you met a group comprised of all your best friends and worst enemies. With your visage and voice disguised, you were invited to stand before them and give a speech. What would you say? Would you single some of them out or give a message designed for the entire group?
Nearly as important as what your character does while in disguise is how and when he or she is unveiled. You must unveil or at least partially unveil a character to please an audience, even if the person who learns his or her true identity doesn't survive to tell anyone else. It is absolutely vital to the vivacity of your work.
And so to you who know me best: write on!