Signlessness seems to be contradictory to Buddhism Signlessness is a concept that I was taught about Buddhism in a college course on Buddhism. It was defined as "not taking omens to have meaning, whether the omen was good or bad does not matter."

But in the same course I learned the mystical means by which the new Dali Lama was found. They see letters in sky telling them to go to Ando Province.

Maybe this is right-mindfulness(?): we see things as they truly are in reality and do impose logic onto things were there should not be. Like if I see my lucky number right as I have that really good feeling when I know I am making the right decision. Must I regard seeing my lucky number as just a coincidence and not a sign?
As I understand it, in Mahayana, signlessness (animitta) has nothing to do with omens. To quote Wikipedia,


  Signlessness refers to the fact that phenomena seem to possess their
  apparent qualities by way of their own nature, but when one examines
  this appearance one realizes that all qualities are merely mentally
  imputed and not a part of the nature of the objects they appear to
  characterize.


Basically, signlessness means not getting caught into traps of abstractions. This is based on clear understanding that real world is infinitely more nuanced and multifaceted than any concept, however precise, can ever dream to capture. There is an infinite number of alternative ways of describing the world -- each valid in its own context.

The notion of signlessness is related to aniketa-cārī (usually translated as "wandering without a home" but having a broader meaning in Mahayana) -- the practice of "non-abiding", or not settling on any single conceptual, metaphysical, or philosophical base.