A few quotes from the Rabbi on 'Redemption of Israel'
in which he teaches that the psalm "As the hart panteth" is recited on Sukkot because our exiled spirit thirsts in Diaspora.
The reason that Sephardim customarily recite the psalms "Like a hind crying for water" and "Judge me, O Lord" before the Arvit evening prayer is that it is followed by "My soul thirsts for God, the living God; When will I come to appear before God!" The intended meaning is: When will the Lord once again grant the privilege of going on pilgrimage to the Temple as in ancient times… Now, in particular, that we are in exile "our souls thirst for God". When will we go – meaning, when will our Temple be rebuilt to come and "appear before God"?... The reason we also recite the "Judge me" psalm is because of its close connection to the one preceding it, that says: Send forth Your light and Your truth…". 'Your light' is the Messiah King, who is likened to light, as he is in the verse "I have prepared a lamp for My anointed one" and 'Your truth' is the Prophet Elijah, the true and faithful prophet, "…they will lead me; they will bring me to Your holy mountain, to Your dwelling place".
Keter Yom Tob, Chapter Seven, Sukkot Festival Customs, p. 2, G.K. Institute Publishing, 1998