Even with the first bomb I wonder if they could have handled it a bit differently. Maybe scuttle a ship with it in the middle of the Tokyo bay, then drop a dud bomb directly onto the imperial palace with a warning painted on it. Seems like immediately after the bombings in hiroshima and nagasaki there was still quite a fog of war going on initially about what even happened. Making the sun appear in the middle of the tokyo bay would have been indisputable however. You'd get the blinding flash, the shockwave, the awe of the cloud, and everyone including everyone in government would not only witness it (anywhere with a window would have gotten the at least the flash), but survive, and do something about having witnessed it.

Of course 1940s thinking of the world was a bit less restrained when it came to the question of wasting a quarter million people in an instant. One wonders if the US felt the bombs were necessary to use with the war already won by that point to have sort of established precedent to use them in future conflicts. The quickness between targets would say as much as well: this is just another bombing run no different than an incendiary run a few days apart from another. After all, that's exactly what MacArthur intended to do in Korea. They were probably desperate to ensure their miracle weapon, one that took so much investment and effort and had so many careers staked in its success, would not end up like chemical weapons where it was verbotten to use even by the nazis.

If the need was /just/ to demonstrate the existence of a second bomb implying a continuous pipeline/supply, that didn't have to happen in a city.