You really need to check the basking area with a thermometer to see how warm it is. Two lights, a UVB light and a heat light over the basking area, are optimal so that the turtle will want to bask (heat) and so that the turtle will get UVB rays (the window filters out the UVB rays so that all the turtle gets is the heat).
How long is the tank (and basking area) exposed to the sun? As a general rule, it's not good to keep a tank near a window. If the weather is hot, the sun will raise the temperature too much. And at the very least, you're asking for an algae problem. That said, I do have one painted who has a stock tank that's exposed to the sun in the winter, but since it's cool in the room he's in overheating isn't an issue and there hasn't been an algae problem.
I'm not certain why your turtle is keeping his eyes shut. (And from what you've written, it's not clear to me how much he's doing it.) If it's really noticeable to you and if this behavior is totally out of the ordinary for him, he could be starting to get ill or something could be irritating his eyes (but if the other one is OK, this would be less likely).
You have separated them?
