The publisher is typically the company that holds the copyright to the musical composition (i.e., the music, but not the lyrics). You can usually find the publisher information on the copyright page of the sheet music or on the album liner notes. If you can't find the publisher information, you can try searching for it online.
The Harry Fox Agency:
The Harry Fox Agency is a mechanical licensing agency that represents many music publishers. You can search their database of songs to find the publisher of "Gotta Be Somebody". Once you have found the publisher, you can contact them directly to request a mechanical license.
The Copyright Office:
If you are unable to contact the publisher directly, you can also try contacting the Copyright Office. They can provide you with information on how to obtain a mechanical license for the song.