The library file has pointers to each song that includes the exact path to it.
It finds the song Cafe 1930 from Al Di Meola plays Piazzolla on my external drive named Music 1 by following this pointer to the song in Music 1/Al Di Meola/Di Meola plays Piazzolla/Cafe 1930
key>Location file://localhost/Volumes/Music%201/Al%20Di%20Meola/Di%20Meola%20Plays%20Piazzolla/02%20Cafe%201930.m4a
....so if any of that info changes iTunes can't find it.
If you change the name of the backup drive to the exact name of the original drive and the folder structure is the same it may be able to find them. I have never tried it so can't say for sure.
You can always delete the original library and just drag and drop the backup drive into iTunes and it will rebuild it, but you will lose play lists and ratings and other stuff that isn't tagged to the songs.
It finds the song Cafe 1930 from Al Di Meola plays Piazzolla on my external drive named Music 1 by following this pointer to the song in Music 1/Al Di Meola/Di Meola plays Piazzolla/Cafe 1930
key>Location file://localhost/Volumes/Music%201/Al%20Di%20Meola/Di%20Meola%20Plays%20Piazzolla/02%20Cafe%201930.m4a
....so if any of that info changes iTunes can't find it.
If you change the name of the backup drive to the exact name of the original drive and the folder structure is the same it may be able to find them. I have never tried it so can't say for sure.
You can always delete the original library and just drag and drop the backup drive into iTunes and it will rebuild it, but you will lose play lists and ratings and other stuff that isn't tagged to the songs.