I'll be bold here: here's the correct way Metallica recorded and plays the harmony part in their Fight Fire with Fire song off of Ride the Lightning album, both guitars included. I have listened to multiple versions: studio, rehearsal, demo and live and YouTube, of course, has been of a great help with this. What I came up with is, in my honest opinion, the real way it is played. It is different in several places from the songbook published by Cherry Lane Music.
I'm pretty sure the harmony was recorded by Hetfield alone - until Load or Re-Load, Hammett used to record only solos. Live, they do it together, of course, with Hammett playing the higher part.
The tabulature might not show the same fingering positions they would choose. It's just the way I play it. However, it's the sound that matters.
Hi-rez PDF file.