I have always understood this song to be a plea to not be the kind of people God condemns for their hardened hearts that cause them to not hear or see as in the passages from Isaiah and Ezekiel, but then I found it also is in Ephesians in the positive sense:
I pray that the eyes of your heart may be enlightened in order that you may know the hope to which he has called you, the riches of his glorious inheritance in his holy people.
~Ephesians 1:18, NIV
In fact, this is the verse that inspired Paul Baloche to write this song. You can read the rest of that story here.
Open the Eyes of My Heart
Written by Paul Baloche
Open the eyes of my heart, Lord (Psalm 119:18, Isaiah 6:9-10, Ezekiel 12:1-2, Matthew 13:13-17, Acts 26:16-18, Acts 28:25-27, Ephesians 1:18)
Open the eyes of my heart
I want to see You (Exodus 33:18)
I want to see You (2x)