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.

True but he wasn’t ruling like the kings of old. Parliament was the governing body and was very powerful even if the king still retain more power of redress and authority than he does today

Seems to be common at the extreme levels of wealth