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Why isn't the battle location used on the map? According to the concept of the "arena" mode, it should be present on the map. This would allow playing with AI, and the attack would occur automatically when both players finish their turn (they would be teleported to the battle location, and one of them would automatically attack). You just need to place the battle location in an inaccessible area for the players and separate the players themselves with impassable obstacles.
For example, I'm attaching a version of the map from the first post with a battle location. I also disabled angel wings there, as they can break the map/interrupt the AI. By the way, it's also playable against the computer.