King George III didn't start really start showing symptoms of mental illness until 1788, and it was only during temporary periods until 1810. There had been a brief episode in 1765, but it was poorly documented, and is described more like a depressive episode than the mania he suffered later in life. All the same, during the period leading up to and during the American Revolution, he was his regular self.

It's also worth noting that by this point in time the monarch was not really the decision maker for most affairs of state. While he was likely the most politically powerful monarch after the Glorious Revolution, Parliament was nevertheless still calling the shots.