This question is about backing up my iTunes Library on a external h/d (G-Drive) with Thunderbolt connection with my Macbook Pro.

TM will not back up the drive it is on.

You could do that if you want to do that kind of backup. A true backup is making a copy on another drive since a common source of data loss is drive failure or drive loss (your house gets broken into and somebody steals all your computer equipment sitting there on the table).

You say you "redirected iTunes the iTunes path for media files" and deleted the library from your internal drive.

Terminology. A "library" is everything in your iTunes folder. If you moved only media to the external an deleted the library (=iTunes folder) from your internal drive your iTunes would now not be working because a functional iTunes is media + a whole bunch of support files and folders.

Since we're not using the same terminology I am not sure exactly what it is you have where. Basically if you want to back up everything you need to make sure you have a second copy of all iTunes related files and you will have to determine where you have all those.

What are the iTunes library files? - http://support.apple.com/kb/HT1660

More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management

What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html

Where are my iTunes files located? - http://support.apple.com/kb/ht1391

iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847 - plus supplemental information about organizing to new structure https://discussions.apple.com/thread/6477809?answerId=26404702022#26404702022

Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/docs/DOC-7392 and making an iTunes library portable.

As regards to the last link and"portable", it is best to not split your media and other library files unless you have a very specific reason for doing so. It makes re-constructing your library more difficult in case of a drive failure and in some scenarios it is more likely to lead to broken links ( ! ).

jfmatias wrote:

So should I just delete the original iTunes library backup on external h/d G-Drive (when my iTunes media library was on my MacBook Pro) and manually backup my iTunes medial/music library now on the external h/d G-Drive on the same G-Drive?

No. You do not backup anything on the same physical drive it is stored on. You backup to a completely differnt drive.

You should have 2 external drives.

One for Time Machine (or other backup application) backup and one for other data (such as the iTunes folder not used on the internal).

Time Machine or other app will backup the internal AND the external with other data.

You can back up to the same drive but it is of limited use. For example, I once had a bad sector on a drive. A second copy residing on a different part of the same drive would have been unaffected. If a file becomes corrupted during writing a copy elsewhere on the same drive would likely remain unaffected.

However, there's bunch of scenarios where only having a second drive works for backup against loss.