Wit was gone from the top of the carriage. Another man sat there instead, a younger fellow in brown trousers and a white shirt, a cap on his head. He pulled that off, looking embarrassed.
"Oi’m sorry, sir," the man said. He had an accent Kaladin didn’t recognize. "He paid me well, he did. Said exactly where Oi was to stand so we could swap places."
"What’s this?" Adolin said, climbing from the carriage and looking up. "Oh. Wit does this, bridgeboy."
"Likes to vanish mysteriously," Adolin said.
"It weren’t so mysterious, sir," the lad said, turning and pointing. "It was joust back there a short ways, where the carriage stopped ‘fore turning. Oi was to wait for him, then take over driving this here coach. Oi had to hop on without jostling things. He ran off giggling like a child, he did."
"He just likes to surprise people," Adolin said, helping Shallan from the carriage. "Ignore him."
The new carriage driver hunched down as if embarrassed. Kaladin didn’t recognize him; he wasn’t one of Adolin’s regular servants.
Words of Radiance, chapter 55
Just a friendly reminder, Shallan changed their destination after leaving Sebarial’s mansion (Adolin was originally taking her to a winehouse), so Wit didn’t have a chance to set up a switch by the menagerie.
In other words, when Wit gets bored of making fun of lighteyes he disguises himself as a servant and makes fun of himself.