How did the twins trick the ghost and outwit him once again?

If you think about the story as about a kind of culture clash between the British and Americans, the fact that the children are able to outwit the ghost suggests that their exuberance is an expression of American iconoclasm. The children love to break the "rules" of ghost/human interaction by playing practical jokes on him, and Sir Simon is at a loss about how to proceed. His final, best trick, in which he appears as the headless Earl, is once again thwarted by the children, who drench the ghost with a bucket of water perched at the top of their bedroom door. Sir Simon gives up trying to scare these children; none of his tricks, it seems, can do anything to affect their love of mischief.

The twins see the ghost as a figure they can torment and tease for their own amusement. They shoot at him with pea-shooters, set up wires to trip him, and frighten him by creating a fake ghost out of a sweeping brush and a hollow turnip. Finally, Sir Simon plots to get back at the twins and scare them by appearing as the Headless Earl, Reckless Rupert. He plans carefully, spending three hours getting dressed up in his famous costume.
However, the twins manage to outwit him once again! As he flings the half-open door to their bedroom wide open, a bucket of water the twins have placed at the top of the door falls on him. That is the final straw, and the crushed Sir Simon gives up all hope of frightening the Americans.