I first encountered a tonneau cover on a Triumph TR3 sports car in 1959. I was never so impressed with anything in my life, though at this juncture I can’t really say why. After all, it was just a rubberized canvas cover that fit over the cockpit. The driver used to unzip his side and fold it down behind his seat but leave the other part attached.
Literature dealing with the idea said that this would reduce buffeting in the airstream of an open car and retain the heat from the heater. You could also hide your luggage under it from the sun and prying eyes. I just thought it looked cool.
It turns out that the name is derived from the French word for cask or barrel and that it was associated with a style of automobile body in the early days. Some of the open rear passenger compartments have a barrel-like appearance and indeed some are even accessed from the rear of the vehicle rather than the sides. When not in use a tonneau cover kept the seats free of dust. The body style is high and imposing and must have been quite a fun place to ride along rutted early roads. Sort of like a bouncy castle.
Nowadays the name is most frequently used to describe the cloth cover for a ute body. These are actually pretty cool in themselves if they are stretched out over two bow frames across the bed. I used to sleep under mine on the occasional country trip and it was as waterproof as you needed. The attachment with bungee cordloops over buttons was a little naff, but it lasted for the life of the ute.
This tonneau seen at Gillam Drive uses punch buttons to secure the perimeter of the cloth. It is as shapely as needs be, though the area it encloses is quite large. It’s a lonely sort of accessory, though, as it just underlines to the driver that they don’t have someone in the front seat to talk to. Maybe that isn’t as cool as it used to be.