Dwayne first appears when everyone on the Biendeltown Express is having dinner. He approaches Lulu and Lou when the former is having tea and the latter is about to eat a cheeseburger. Lulu recognizes Dwayne, who asks her if she's really here, and she assures him she is. Lulu tells Dwayne that she hasn't seen him in years, and he then tells her that she doesn't look a day older than when he last saw her. As he kisses her hand, Lou shouts "Ahem". Lulu introduces Lou to Dwayne, telling him that she and him used to see each other quite a bit ages ago. A jealous Lou tells Dwayne that he is Lulu's husband. Dwayne tells Lou it's nice to see him, and tries to shake his hand, but Lou refuses to shake back, telling him that Lulu is his wife now.
Later in the episode, when Didi tells the rest of the adults that if they all took turns watching the children, the rest of them could enjoy the sights, Dwayne walks up to them, carrying a tray of drinks. He tells them that he thought they could use a nice, cool drink, then looks over at Lulu, who takes a glass of water from the tray and thanks him for it. As an angry and jealous Lou takes a glass of water from the tray, Lulu tells him to be nice to Dwayne.
That night, when Tommy, Chuckie, Phil, Lil, and Kimi chase a mysterious figure to the back of the train, they pull the emergency cable, thinking it would open the door the mysterious figure went behind, but it only stops the train instead. When all the adults find out about this, Lou tells them that Dwayne must have been responsible for stopping the train, only to be proven wrong by the conductor seconds later.
The next morning, two detectives board a train to help the adults search for Minka's necklace, which went missing when the train went through a tunnel the day before. When one of them asks the adults to report any suspicious activities they may have witnessed, Lou tells him that he never liked Dwayne's looks. Dwayne then comes up to the adults with a tray of coffee, and asks if any of them would like any coffee. Betty tells Dwayne she'd be happy to have him serve her coffee, which he does for her.
Towards the end of the episode, after it is revealed that Jonathan was the mysterious figure that boarded the train, one of the detectives walks into the baggage car and looks at a tag on an open suitcase. The tag reveals that the suitcase belongs to Dwayne, and when the detective looks inside the suitcase, Minka's necklace is revealed to be in it. Dwayne is promptly arrested and handcuffed, and as he is taken away, Lou tells Lulu that he was right about Dwayne not being any good. When they stop at the next station, the detectives take Dwayne away and into custody.
You can find Dwayne Tickerbacker gallery here.