"With his closed eyes" vs "With his eyes closed"

Context: (Sherlock Holmes and the Duke's Son / Oxford University Press)

He was a large man, tall, well-dressed, and important-looking, He came into the room, walked to one of the big chairs, and suddenly fell into it. He sat there, with his eyes closed, looking white and ill.

Can we say "with his closed eyes"? instead of that sentence.
And what's the difference between them?

There are slightly different meanings.

He did something "with his eyes closed" means that his eyes were closed while doing it.

He did something "with his closed eyes" means that he used those closed eyes in doing it.

Since there isn't much you can do with your closed eyes, the term isn't used much.