Rex R. answered 04/26/19
Writer, public speaker, and visual storyteller
"His eyelids fell shut" makes more sense, but I don't think I've read either phrase in a published text. If you're looking to branch out in your writing, try changing the subject of this sentence from "his eyes" to "he." You could also make the subject an object or scene that the character is looking at, thus showing the character's perspective – right before he falls asleep.