Where on the negative-positive scale should we strive for our thoughts to be? As positive as possible? As negative as possible? Some balance? What's the balance? Or should we just think however we automatically feel like thinking?
One should strive for them to be accurate reflections of the situation at hand, providing one is capable of using that information and handling the emotions properly. For instance, if a situation is crappy, then it's rational and realistic to feel negatively about it. However, if a person can't handle that because it's too much and causes them to fly off the handle into a depression, then a more positive mindset - whilst delusional - would probably be a better reaction. If a situation is good, it makes sense to feel positively about it.

But it seems like more than that. It seems like, while being critical and negative I'm able to think more deeply, more clearly, I'm able to uncover truths about things that I wouldn't while happy. Any thoughts on this?
Critical scrutiny is itself a negative reaction because that involves the consideration of the possibility that something is wrong. It's very hard to feel positive about that, unless one takes pleasure in proving something wrong, though there are times where this is the case, and is an understandable and reasonable reaction.

Negative emotions also tend to be a motivator for change, which leads towards you becoming happier. If one is happy then of course one is less likely to think clearly because the questions asked might cause the person to realise something is wrong and thus lose their state of happiness, so there's less incentive to do it. Unless someone is depressed, I don't think unhappy people intentionally overlook things that will make them happy, whereas happy people do overlook things that might make them unhappy.