That's impossible because the notes clearly state that the Great Engineer took the Aetherlight with him.
The small lantern that the Scarlet Man is so often depicted holding is the Aetherlight. Why? Because that's the only thing that makes sense.
The Great Engineer is depicted carrying it as he leaves the city here:
I personally believe that, staying with the Biblical allegory, the Scarlet Man is the Great Engineer in disguise, but many have denounced that theory.