Enlightenment: Part Two

Captain Striker and his officers reveal themselves to be Eternals, mind-reading creatures who live outside of time and who require Ephemerals (humans and other "time dwellers") to relieve them of their emptiness. They race against other Eternals for the grand prize of Enlightenment, by which to grant their deepest wishes. That can't be good for the universe, but how can the Doctor strategise against beings adept at reading his every thought?