I have not actually finished reading the series myself (I was reading the pre-existing translation for a few volumes but decided I'd rather not have it influence my work), so I don't know if more is explained about Gary.
I notice on page 13, the window has the パッパー sound effects (which I'm not really sure how to explain in English, based on what I've read about it... It's like a "sound effect" for bright light, when it makes a grand change in scenery or something, I don't know if English language comics have an equivalent), which point towards maybe what woke him up. It seems like maybe he had a concerning dream? Or maybe he didn't mean to fall asleep, so the hand over his mouth is just him realizing he missed something? I'm not sure, I can only assume it's left open for interpretation at this point.