In Book 6 of Mika Waltari's historical novel The Egyptian, Kaptah, Sinuhe's slave and companion, ascends to the throne of Babylon for a day:
I was by now familiar with many customs in Babylon, yet I was astonished to see the King’s bodyguard before dawn on that day crowding drunkenly into Ishtar’s House of Joy, breaking open the doors and striking everyone they met with the butts of their spears as they shouted at the tops of their voices:
“Where is our king hiding? Bring him forth speedily, for the sun is about to rise, and the king must dispense justice to his people!”
But when they had had enough of mockery, they released me, saying, “Waste no more of our time but deliver to us your servant, for we must bring him to the palace with all speed, today being the Day of the False King. It is the King’s will that we hasten to the palace with the man.”
When Kaptah heard this, he was so terrified that he began to tremble and shake the whole bed so that they found him and, dragging him forth with jubilation, made deep obeisance before him.
They said to one another, “This is a day of great rejoicing, for at last we have found our king who had hidden himself and disappeared from our sight. Our eyes are gladdened by him, and we hope he will reward our fidelity with many gifts.”
Waltari, M., & Walford, N. (2002). The Egyptian: A novel. Chicago: Chicago Review Press.
Wikipedia claims the event has "its basis on reality", and points to Rajala's Unio mystica: Mika Waltarin elämä ja teokset for evidence. Unfortunately, I couldn't find a translation and cannot verify the claim.
The "day of the False King" appears to be central in Brad Geagley's novel Day of the False King, and the novel's Goodreads description also claims that it has a historical basis:
As in "Year of the Hyenas," most of the events and characters in "Day of the False King" are drawn from history. The Elamite invader King Kutir and the native-born Marduk truly vied for the throne of Babylonia. There really was a festival called "Day of the False King," when the entire world turned upside down for a day, when slaves ruled as masters, when the most foolish man in Babylon was chosen to become king. Semerket the detective is plunged into the midst of these events in pursuit of his own goals: to serve his Pharaoh and to find the woman he loves.