how long does it take for a guinea pig to get comfortable enough to sleep with its eyes closed?

Answers:
I have read that guineas don't typically sleep with their eyes closed and that they can be in a sleep like state with their eyes open. Maybe you are missing the short times his/her eyes are closed. I have two guineas (one I have had for 3 years and the other one only 4 months) and find the above to be true of mine.
This website goes into further detail www.guinealynx.com

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If your guniea pig is too stessed to sleep with it's eyes closed I'd move it into a quite room and cover the cage, then leave the poor little tramitized animal alone until it adjustes to it's new surroundings.

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I run a guinea pig rescue, I can have as many as 40 in my home at any given time, they are always coming in and out, the new piggies go to sleep here and have always closed their eyes, so it would be safe to say immediately

ADDING

Do you have a hut or straw home for him to get into? Adding one might be a good idea, and the answer before mine, has a really good point, quite spaces also help