Does Arcane Signet count as a mana ability or a triggered ability when it's tapped?

Arcane Signet's tap ability reads: '{T}: Add one mana of any color in your commander's color identity.' This is an activated ability (it has a cost separated by a colon), and specifically a mana ability under CR 605.1 because it meets all three conditions: it is an activated ability (not a triggered ability), it could produce mana, and it does not have a target.

A triggered ability begins with the words 'when,' 'whenever,' or 'at' (CR 603.1). Arcane Signet's ability has none of those words — it is activated by paying the tap cost, so it is definitively an activated ability, not a triggered ability.

Because it qualifies as a mana ability under CR 605.1, it does not use the stack (CR 605.3a). This means opponents cannot respond to it with instants or abilities the way they could respond to a spell or non-mana ability. It resolves immediately when activated.

Concrete example: You control Arcane Signet and tap it to add {G} to your mana pool to help cast a creature spell. Your opponent cannot respond by destroying Arcane Signet before the mana is produced — the mana ability resolves instantly without using the stack, and you get the mana regardless.

Relevant rules: CR 605.1 defines mana abilities; CR 605.3a specifies they don't use the stack; CR 603.1 defines triggered abilities by their 'when/whenever/at' wording.