Sorry to tell you this but your tree is probably doomed:

http://www.kesq.com/news/fungus-kills-local-pepper-trees/21237222

What you have is probably Oak root fungus which resulted from the tree being neglected for so long. Pepper trees are not particularly susceptible to this disease, but if a tree is allowed to grow big and then suffers a prolonged drought, there will not be enough water to sustain the entirety of the tree and some of it will die. The fungus can then take hold on the dead wood, and once the tree has contracted the disease it is too late. (Proper maintenance involves removing dead wood from the tree)

https://www.kcet.org/socal-focus/when-pepper-trees-shaded-the-sunny-southland

Emily, is there any chance yo could provide us a picture? Any tree can have a dead limb or two. It is not automatically the death sentence described above. But do realize, what is dead will remain so. There is no way to get bark to regrow on a dead limb or leader. That ain't happening. But it could be that those parts could simply be pruned out. It might amaze you what a good, judicious pruning can do for a tree. But a photo sure would help.

i would plant a replacement tree ... so when the first fails.. you have some years invested in the new one ..

need pix

ken