Rather than post the version I heard from my dad as a little kid, I’ll point to Knows and Knows Not (variations) where there are several ways of saying the same basic ideas.
Using people in the news or pop culture, try to come up with examples of these four types.
My Mom used to say, “Show me your friends and I’ll tell you what you are”. I did not want to hear it back then but it is as true today as it ever was. 
“He who knows not, and knows that he knows not” - I’d say that’s the real wise man.
“He who knows and knows that he knows” is competent at best, or arrogant at worst.
And when was that website from, 1995?
I can’t add to your knowledge of that website’s age, but I can say that I heard a version of this thing in the 1950’s and it was old even then.
I’ve never quite understood the subtle differences between these types and do tend to agree that the “wise man” usually comes off as a jerk.
But the fool, sleeper and ignorant guy are all fuzzy to me.
That’s why I was looking for some interpretations from you folks.
There could probably be some other variants on the theme such as:
– He who knows not and doesn’t give a shit that he knows not, is electable, vote for him.
– He who knows and wonders why he knows, is confused, buy him a drink and send him on his way.
Others?