Howdy Wayne,
It is more likely to be Weaver's Needle than any thing else, when you consider that the doodle was made by Jacob Waltz, and his clues revolve around it. A name is not needed when you can see that it's a perfect match.
Panoramio - Photo of Weaver's Needle from the north
I would like to see other peaks which have that same profile.
If we don't know for a fact, that everything on the page should be viewed from the same location, why is it accepted as the gospel when coming from Jack San Felice, and why can it actually be Weaver's Needle when this clue is tried to make fit the Pit Mine?
The so called "gunsight" clue is in fact referring to the doodle left by Jacob Waltz. It is not a completely different clue. I could not find the name of the person who started to call it like that, but since Joe Ribaudo doen't lie, he could tell you who coined that phrase. Here is a quote from Joe:
"Someone who's opinion I respect very much gave the view from the mine the "gunsight" name."
I'm sure you can take that to the bank.

He was referring to Jacobs doodle at the time. If you look closely at Weaver's Needle from the Pit Mine, the profile is reversed, so again, that clue doesn't fit at all.
Joe,
Jacob Waltz was not dying at the time he drew that map. It is said to have been made probably a month before his death, while trying to show Rhiney Petrasch how to get to it.
Homar