Davis's karmic eyes only lasted two seconds. He activated it before comprehending the general direction in which Shirley was before he turned it off.
The Death God Eyes and Karmic Sight were two different techniques he utilized. At first, he needed to use Fallen Heaven, but now, there was no need since, after many uses, he instinctively knew how to use it. It was as though they were a part of his soul, no different than feeling the hairs on the arm or realizing that he was breathing after it was being mentioned.
He could just activate these mystic ocular techniques with just a thought.
Naturally, he knew there was a great difference between the ocular techniques using his energy and using Fallen Heaven's energy. It went without saying that he could see more using the latter.