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To clarify, even if you know where the hero(es) are in the discard pile, Sing and Praise would still require a search and would be stopped by Hezekiah's Signet Ring.
I believe the two "specific locations" of the draw pile are the top X cards and the bottom X cards. For example, using Astrologers to reveal the top or bottom card is not a search even though it's targeting the deck. Likewise, Divination is not a search because it is targeting the top 6 cards. Theoretically, a card like Susanna could even reveal your entire deck if it's small enough at that point in the game, but that is still not a search ability, it is a reveal.
The discard pile is a known location but Hezekiah's Signet Ring still restricts