In a showdown, if Player A passes Focus, then Player B activates a rune's Add ability and passes Focus, does the showdown immediately close, or does Player A receive Focus again? Does activating an Add ability reset the consecutive-pass condition? Relevant rulings: Rule What it establishes 164.2.a Exhausting a basic rune for Energy is an activated Reaction ability. 430.2.a An Add ability doesn't pass Focus or Priority. 347.2.a The showdown ends when all players pass Focus in sequence. 348 The showdown closes when everyone passes without playing a card or activating an ability. 347.2a makes it sounds like the showdown ends because there were 2 passes in a row. 348 makes it sounds like the showdown continues because someone activated an ability Has there been an answer to this one on an official channel?

No — the Showdown closes; Player A does not get Focus back, and activating an Add ability does not reset the pass sequence. Rule 430.2.a is the tiebreaker between the two rules you quoted: an Add ability finalizes and resolves immediately and "Priority and Focus will not pass from Add abilities being finalized or resolving." It never enters the Chain, so it isn't the Rule 347.1 action (a legally-timed card or ability that starts a chain and hands Focus on under 347.1.b).

That's also how 348 and 347.2.a fit together — "without playing a card or activating an ability" means a chain-starting play, not a Limited Action like Adding. So A's pass and B's pass are still consecutive, 347.2.a is satisfied, and the Showdown closes right there (Combat Showdown → damage step then Combat Cleanup; Non-Combat → Control/Conquer for the sole player left). If B wants to keep the Showdown alive, they have to actually play a card or activate a chain-starting ability, not just top up their rune pool.

On your last question: there's no published FAQ entry answering this exact interaction. The closest official text is Core Rules 430.2.a (Add and Focus/Priority) read with 347–348, which is what the ruling above rests on.