Kate will find that the spirit is wandering around the Grey Zone park area. This is good; it hasn't really come into contact with many people yet because few are stupid enough to take a park. for the most part, it seems to be wandering aimlessly.
Once Kate stops focusing on the spell, she should be able to walk directly to the spirit, and if its location changes, so will the mental pointer that's taking her in the right direction. Until she chooses to drop it, that is.