Sorry that this reply is almost 2 decades late, but that awesome pub jig the author's talking about is a movie remix of the song "Irish Soldier Laddie"

https://www.youtube.com/watch?v=qvmDYAY9LPA

The essential melody is the same, the bridge of the song has been changed to the main melody for the Patriot Games version. Ken O malley, The Blended Spirits and Padraig Duggan composed and performed it and it was indeed called "The Pride Of Our Land."

All the lyrics I could catch are

"Here's to you, my brave Irish Laddie, we'll not be broken, downhearted and sad, so let us make a toast, to all of our comrades, same for the honour and pride of our land.

We'll sing you a song, from the land of our fathers, a song I could tell you have come to hear me play

They came to destroy the pride of our nation ----"

The Pride Of Our Land hasn't ever been released sadly, from what I understand with a bit of inside knowledge, it was just drummed up specifically for the scene, using Irish Soldier Laddie as the basic melody

Hope this helps