At first look this proverb seems to make two statements that do not match one another - but actually both parts of this proverb speak to the same thing - hypocrisy. One speaks of hypocrisy with the actions - while the other speaks of it with words.
When someone winks the eye - it means that they are sending a sign with their eyes that betrays the words or actions that they are about to say or do. The wink is not for everyone - but only for those they desire to be in the know about the coming hypocrisy of their statement or their action. The person to whom their words are said is kept in the dark. It is almost as if the hypocrite is saying to the person, "Watch what I do to this fool. You will find that what I am about to do is funny or clever." When you have a "winker" you basically have someone you cannot trust. If they lied to this person - they can lie to you. If they are seeking to deceive this person - they will deceive you. We are told that the "winker" does what he does to cause trouble. He winks at you - but he only does so to make you an accessory to the crime. Now that you are in the know - you too are aware of the hypocrisy - and your job now is to laugh behind the scenes - but to help maintain the hypocrisy by your silence and complicity.
We read in the second part of this proveb that the "babbling fool will be ruined." The "winker" is the "babbling fool." They are one in the same. The babbling fool deceives with his mouth - the "winker" with his eyes. But in the end, both of them are fools because they are walking in deception. They have no good in their desires for the one they try to deceive. And like all those who babble as fools - the day will come when their duplicity will be exposed. On that day they will be thrust down - humbled and that with severity.
When someone winks at you - and does so to cover an malicious action or unkind thoughts and words toward someone who is not initiated into the mess, we should reject their invitation to enter into the hypocrisy. As an example we have Judas who did not reject the hypocrisy of the Pharisees and Saducees. He chose to betray Jesus for 30 pieces of silver - and promised to betray Jesus openly. The sad end of that story is that Judas did sell Jesus out for the price of a slave. He did so as He maliciously winked - or as was the case in his betrayal - he kissed Jesus on the cheek. There was no love or fellowship in that welcome - only open betrayal. That is why we need to be men and women of truth - and reject the call to enter into other's treachery when winked at and encouraged to betray others.