Do Geases (old or new) work on the undead?
Yes. They have twisted souls that are bound into their corporeal bodies, but the soul is still there. The exception is for Zombis created by the Samingan Zombi Attunement – the soul upon which the Geases were placed is fled, and the body is nothing but walking meat. Failed Mummies have the original soul bound into them, and so Geases should remain.