All 3 Uses

mystic
in
Flags of Our Fathers
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She felt an almost mystical connection to her boy because, as she was telling everyone, he was in the famous photograph.†
Chpt 15. *

mystical = relating to realities beyond scientific understanding OR inspiring a sense of wonder or mystery; or beyond human comprehension
As the Seventh moved toward its May 9 kickoff in Washington—it would storm through thirty-three cities before winding up back in the nation's capital on July 4—The Photograph's mystical hold on the nation continued to deepen.†
Chpt 16.
I was hypnotically drawn into this old land, into what struck me as an almost mystically refined, cultured society.†
Chpt 20.

Definitions:

(1) (mystic)
a person who seeks or claims to have direct spiritual insight beyond ordinary understanding; or describing an experience that feels deeply spiritual, mysterious, or otherworldly

In common usage, mystic is more likely to be used in reference to a practitioner of a less mainstream religion than a more mainstream religion -- possibly because the former is more mysterious to the writer.
(2) (meaning too rare to warrant focus)