It for sure sounds like there is a lot more going on than the child is just overtired. The blank periods could very well be epileptic seizure periods and to a certain extent it sounds like a child that has suffered a mild stroke which yes is more common than we think.

One thing you could do is document sort of a point form notes so to speak of things that you have observed and give it to the parents with the idea that you area new on the scene and haven't had the background time with this child and that you were compiling the list to discuss with the parents in the future but are giving it to them now as they leave.

What they do with it will be up to them. Hopefully they read it, start to look for the same things and share the info with their doctor.