No, its not a piano its a GUITAR - Over many seasons I've tried to find out the name of the piece, and never been successful.
And it did play during the Catalina date - just before they went inside the big tent, to get out of the rain which was just beginning to fall. I think its either just before he tells her to keep quiet, and just kiss him - its right around that segment. On the tape I viewed, the timestamp on the bottom of the screen read 8:25 /12:10.
If I'm wrong, then I stand corrected and apologize for my error.