In 1924, a young man called Joaquín Argamasilla
demonstrates his supposed X-Ray Vision power to a small crowd of important people of the time, such as writer Ramón María del Valle-Inclán, to whom it is also announced that Argamasilla will soon travel to America to repeat his demonstration to no less than Harry Houdini. However, one man in the crowd carries a set of modern glasses: he is a Ministry agent.
Back in the present, the patrol, now recovered from their previous scare, is handed a new mission: Argamasilla is (or was) an agent in the 1924 Ministry of Time, but it is speculated that he may be planning to use his travel to the United States as a cover to sell the secret of the time doors to J. Edgar Hoover, newly minted director of the Bureau of Investigation (the future FBI). To prevent this, the trio must go to 1924 and accompany Argamasilla so he won't betray the Ministry: while Amelia and Alonso act as journalists, Pacino will become "El Gran Benito", who can see the future.
When they arrive, they encounter Argamasilla and his father in a spiritualism session, where "El Gran Benito" uses his knowledge of future events (namely, where the bodies of two murdered children are) to establish his reputation: when they speak with the Argamasillas, Pacino reveals they are going to New York, which the father regards as a coincidence, but the son does not, obviously suspecting something's afoot.
Arriving to New York, Alonso, Amelia and Pacino take rooms in the same hotel as Argamasilla, but soon run into problems as Darrow Ltd. have also sent a team to 1924, but their intention is quite different: they plan to kill Argamasilla so he cannot go through his plan to sell the secret of the time doors. Lola, who is there as well, surreptitiously warns Amelia about what is going on.
Argamasilla meets with Hoover in a speakeasy (whose password is "swordfish"), but he does not manage to get his offer through before Pacino grabs him and gets him out of there: he then reveals that he and his companions come from a future Ministry, and warn him that he must do what he can to prevent people from really knowing whether he actually has X-Ray Vision. If he fails the test Harry Houdini has planned, then Darrow will leave him alone. However, when the time comes for the test (consisting on having ten wooden boxes, with five of them containing a quill: the objective is to pick the boxes with a quill), Argamasilla tries too hard and picks the boxes that do not have a quill, which makes him look even more suspicious.
At a later point, during a celebration dinner to mark Argamasilla leaving, one of the Darrow men enters the party and begins to shoot against Argamasilla, failing in his first attempt. While those present run away, Houdini guides Argamasilla and the patrol to another room, getting them in a wardrobe, entering behind them and closing it before the Darrow man can shoot again. When he does, and opens the wardrobe, it turns out to be empty.
Suddenly, the trio from several hours before have a sensation of déja vu, and Houdini nonchalantly enters the room (apparently, performing Mental Time Travel is an ability of his) while suggesting the group to depart immediately, which they do. Upon their return, Argamasilla is reassigned to the 2016 Ministry (not without checking Irene out, while Amelia brings Houdini to his youth in Hungary, so he can hear his mother speak his name again.
