Can you conquer a battlefield during an opponent's turn (e.g., by using Zenith Blade to win a showdown at an empty battlefield they attacked)?

Ruling: Yes, you can conquer and gain points during any player's turn, including an opponent's turn.

Nuances:

• Even if you control the other battlefield, you still don't win under the last point rule since you didn't score on the battlefield you controlled this turn (unless you conquered that one this turn too)
• If you conquer a battlefield on an opponent's turn and they end their turn, you also get a hold/8th point on your very next turn
• There may be a conflict between rules as written (RAW) and rules as intended (RAI) regarding whether only attackers can conquer battlefields, but defensive conquering is confirmed as possible in rare situations