1 Timothy 2:1
1 Timothy 2:11First of all, then, I urge that petitions, prayers, intercessions, and thanksgiving be offered for everyone—
Watchtower literature accepts Paul's command in to offer "supplications, prayers, intercessions, and thanksgivings concerning all sorts of men" — and Witnesses do pray for the well-being of civic leaders. The verse is not usually paired with 2:2 in the civic-neutrality conversation, because the pairing exposes the gap between praying for civic outcomes and refusing to participate in them.
Keep 2:1 and 2:2 as a single unit. Paul is commanding the Christian congregation to do moral work through intercessory prayer — prayer "for all sorts of men," including kings. If Paul wanted Christians to practise cosmic withdrawal from civic outcomes, he would not have commanded them to pray earnestly about those outcomes. The prayers in view are not passive well-wishing; they are serious intercessions aimed at a specific civic end (2:2's "peaceful and quiet life"). Ask the Witness: can a believer sincerely pray for justice at court, a fair trial for a neighbour, or wise law-making, and then refuse to sit on the jury, testify, or vote for the wisest available option? The prayers of 2:1 do not sit comfortably with the civic prohibitions of the neutrality doctrine.