It might be useful to distinguish between conditions for playing a card and conditions for initiating an effect of the card.
Far Sight, in order to be played, needs a sage and an untapped site. Once it resolves, there is an effect which can be initiated by tapping the sage and the site.
There is also an effect which happens either way (sage makes a corruption check).
All Thought Bent On It, on the other hand, has as its conditions for play an untapped sage and a site where information is playable (quite different from the Hero version, which requires an untapped site). It then has three separate effects:
1) Tap the sage and the site;
2) Search for an Item; and
3) Corruption check.
None of these effects has any active conditions attached to them, so I don't think there's any problem with things needing to be tapped and untapped at the same time.
As a side note, it's indisputable that tapping a card is not always an active condition:
Fate of the Ithil Stone wrote:Tap this card if the company plays a Palantír; this card never untaps.
Nobody in their right mind can argue that tapping Fate of the Ithil Stone constitutes an active condition. Is is an effect generated by playing a Palantir.
Therefore tapping a resource or character is not always an active condition.
Maker's Map requires an untapped Ranger and site as active conditions for its play. I don't think that anybody can reasonably say that tapping the Ranger and the site are active conditions for the +2 to movement rolls through the Under-Deeps. (Konrad: Were you referring to Maker's Map with your post? I think you're right in saying that Maker's Map cannot require as its active conditions that the site be both tapped and untapped upon resolution.)
Given that the rules say resource events do not require untapped sites unless specified
and there are several resource events that specifically require untapped sites, I'd conclude that Secrets of Their Forging does not require an untapped site -- but the site will tap if not already tapped. I would further conclude that without a wording which clearly links tapping the sage and site to any of the effects generated by the card (Replace the Gold Ring Item or Discard the Gold Ring Item (and note that you can freely use this card simply to discard a Gold Ring)), tapping the sage is another effect of the card, not an active condition.
If anybody can put forth a good argument to the contrary, I'd be interested. But Maker's Map is a good case for saying that "tap whatever" is not an active condition unless clearly linked to a specific effect.