The two passages I don't think are related in the way you are asking. The judges passage is a judging of Israelites who are better suited to carry out a task, and though the task is in a way to judge a nation that was against Israel, the Psalm passage is a matter of the LORD judging all nations.
The word in the Hebrew text is better translated probably as GENTILE NATIONS -- all nations other than Israel.
OOPS I MISSED YOUR POINT ABOUT DRINKING. There might be a parallel between the focus on duty of the the Messiah on God's right hand and God choosing those who are focused on the task at hand.
Thanks for asking a rather interesting question that identified in the Psalm a passage of universal application, and that Judges is one of the many historical steps along THE WAY.
I had recently asked a question in regard to Psalm 110 on an issue a couple of verses before, namely the killing by the Lord on God's right hand of the kings of the Gentiles. Connecting to the Psalm verses you refer to might be the phrase "therefore He will lift up His head".
I might also add here to what I said in my question, the head might be as the renewed mind of the believer that is enabled in terms of moving from being a babe on the milk with just the renewed mind, to a fully matured believer with the renewed mind enabled to understand the Bible mysteries.
TO DO THIS INVOLVES PERHAPS OVERCOMING ALL OF THE BELIEVERS REMAINING INDWELLING SINS. The old Gentile or subconscious heart corruption which for a believer with a renewed heart is protected from the evil one by being hid in Christ till he overcomes fully said remaining indwelling sins. The old nature has a kind of hierarchy where there remains yet in that structure a kind of rulership/kingship aspect which is key to facing and overcoming the believer's remaining indwelling sins.
This relates to the mystery in Romans that the fullness of Gentile times must happen before Israel will be added to the church, where Israel is the fully conscious mind that it will become one with the heart mind (the subconscious), where heart and mind are one in the Christ. The first step is a conscious, proper repentance to gain the renewed mind, and an acceptance of the holy spirit as one's teacher to gain the matured renewed mind, which probably is very rare among believers -- among those not yet possessing, such I ... sigh.