Doves, Keel argues from comparative ancient evidence, are messengers of love.  ”Your eyes are doves,” thus, means that the eyes send inviting messages.

Which sparks out in all kinds of directions: The dove is the Spirit, messenger of the Father’s love for His Son, and for us; doves and eyes are associated, so that the dove of the Spirit is sent from the eyes of the Father, the eyes that value us as His beloved; the seven eyes of the Lamb are the seven Spirits, which are the seven doves, which are seven springs engraven on a stone (Zechariah 3:9); our eyes are also doves, sending messages of love, radiating the Spirit that is in us (“brightened eyes” mean refreshed spirit).  Etc.