Book One - The Perennial Child
"The Beach Car"
Randall first appears in the Beach Car, talking to the Cat about business opportunities, particularly as they relate to selling the Donut Holer. He plays a fairly minor role until Tulip decides she wants One-One back, whereupon Randall takes it upon himself to help Tulip by helping her chase the Cat. After landing on the shuttle that the Cat uses, Randall makes droplet clones that drip onto the control panel and short it out.
"The Ball Pit Car"
In Khaki Bottoms' room at the indoor playground Randall is shown to be one of the attainable prizes for completing the challenge. He sits idly in a tall flower vase with a neutral face without acknowledging Tulip or anyone else. Randall's appearance in the episode is the first indicator that The Cat came to the Ball Pit Car before Tulip's group did.
The Train Documentaries
"The Tech Support Car"
One-One shows off Randall working customer service for his donut holer business.
Book Two - Cracked Reflection
"The Black Market Car"
Randall is seen in a video One-One shows to a new passenger.
"The Toad Car"
One of Jesse's photos on his phone is a picture of him and M.T. with Randall in the Beach Car, apparently having encountered him in the car off-screen.
"The Lucky Cat Car"
M.T. and Jesse run into Randall again at a game booth in the Lucky Cat Car, where he works. When they notice Jesse got more points even though Lake won the game, Randall whispers to them that he is required to give more points to passengers as they have more incentive to get out of the car. He then offers them a Donut Holer, which they decline. One of the other Randalls informs him he came on a little too strong.
Book Three - Cult of the Conductor
"Le Chat Chalet Car"
Hazel and Tuba meet Randall while playing with the fountain in the car, with Randall happily indulging them. However, the Cat reminds Randall she hired him to serve as water, not to make conversation. Later, when Hazel makes tea, she is surprised to discover the tea is Randall, with the Cat explaining to the group that all of the water in the car is Randall because the entire car has been in a drought for centuries. Grace puts two and two together and realizes the snowstorm keeping them trapped is Randall, who witnessed them having a snowball fight and wanted to join in. They ask that he stop the snowstorm, which he agrees to by having them boil him (which apparently does not hurt him at all), sending the Randall vapor into the sky whereupon he gets the cloud Randalls to agree to stop snowing.