Thank you very much for your help. Here go some more sentences related to participal construction.

1. He was standing there, and he closed his eyes.
(Did he close his eyes later? Or was two actions done at the same time?)

2. He was standing there, closing his eyes.

3. He was standing there while he closed his eyes.

4. He was standing there, his eyes being closed. (by him)

5. He was standing there, with his eyes closed.
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Are they all the same in meaning? Do we have to add 'by him' in #4?

Sentence 4 is very awkward, but the others are fine. The two actions in each sentence are simultaneous, yes.

I wouldn't use #4.

1. In the first sentence, "He was standing there, and he closed his eyes," it is not explicitly clear whether he closed his eyes later or if both actions were done at the same time. The conjunction "and" leaves room for interpretation, although it might suggest that the closing of his eyes occurred subsequently. To determine the precise timing, further context or additional information would be needed.

2. In the second sentence, "He was standing there, closing his eyes," the closing of his eyes is presented as a simultaneous action to him standing there. The participle "closing" functions as an active verb, indicating that both actions are happening at the same time.

3. The third sentence, "He was standing there while he closed his eyes," implies a sequential relationship between the actions. The phrase "while he closed his eyes" suggests that he began closing his eyes after he had already been standing there. This construction emphasizes the order of events.

4. In the fourth sentence, "He was standing there, his eyes being closed (by him)," the phrase "his eyes being closed" is a passive participle construction. It implies that his eyes were closed by him, although this information is already implied by the possessive pronoun "his." The addition of "by him" is redundant and unnecessary.

5. The fifth sentence, "He was standing there, with his eyes closed," is similar to the second sentence but with a slight difference in emphasis. This construction emphasizes the state of his eyes being closed rather than the action of closing them. It suggests that he was already standing there with his eyes closed, without specifying when or by whom they were closed.

While these sentences convey similar ideas, their specific meanings and nuances may vary slightly. The choice of construction depends on the intended emphasis and the context in which they are used.