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2.3.3 Passing. If a 1st or 2nd Eligible Faction opts to Pass, it remains Eligible for the next card .... The next leftmost Eligible Faction then replaces the Passing Faction as the new 1st or 2nd Eligible Faction and receives the same options to execute or Pass. If the last (rightmost) Eligible Faction Passes, adjust cylinders (2.3.7) and play the next card.
Three factions are Eligible.
The 1st Eligible Faction (Warlords) opts to Pass.
The next leftmost Eligible Faction (Coalition) replaces it as the new 1st Eligible Faction. That much is explicit in the second quoted sentence.
Does the final Eligible faction (Taliban - which started the card neither 1st Eligible nor 2nd Eligible) in turn replace the Coalition as the new 2nd Eligible? That much is not explicit in the second quoted sentence (because Coalition is not "the Passing Faction").
Yes, in this case would be Taliban 2nd eligible.