plot explanation - How/Why did Tyler Durden got shot in the head? - Movies & TV

From the movie Fight Club, in the ending scene we can see the narrator shoot himself in the mouth asking Tyler to "really listen to him"...

The question is How/Why did Tyler got shot in the head when the narrator himself shot in the mouth? It could have been somewhere else and not the head, right?

Is this just because the Narrator "really" wanted Tyler to listen to him and die?

Since Tyler is just a hallucination, we know that Tyler dies when narrator mind accepts his death. The narrator can't do this on his own, since he needs Tyler's permission to do so (otherwise why would he ask Tyler to listen to him?). Now, if he really wanted Tyler to die, he could have shot Tyler directly and imagined his death, which would have lead to the end of Tyler.

Is this shooting scene in the significance of "Fight Club" where the narrator wanted to shoot himself just with the spirit of hurting himself? Does this indicate that Narrator and Tyler became one at the end?

Was that shot really needed to kill Tyler? What would have happened if Tyler also got shot in his mouth and was alive instead of getting shot in his head?

I have attempted the plot-explanation, but I watched the movie only once long back... I would be glad if someone can expand this/ explain this even better.

Answer

The purpose of the end scene of the movie is to have the Narrator finally conquer his 'problems' in the form of killing Tyler.

He cannot simply shoot at him as he is just a hallucination of his own mind and the bullet would just fly off into nothing. While before beating him up would have worked, it was just a physical representation of a mental battle. By bringing in an actual object into the fray, his attempts at Tyler's life are pointless.

We see the Narrator finally realize that he has been in control all along and this is why he is presented able to take the gun from Tyler, because he is the one actually holding the gun.

It is then he realizes that he must follow Tyler's own advice and "hit bottom". Only by doing so, is he able to control his own body and "kill" Tyler. To hit bottom he realizes he must do something life-threatening and plain insane.

Whereas the bullet only blew a hole in his cheek, it was his mental F--- You to Tyler, showing him that he can take care of himself now, which is why the bullet is shown to have gone through the back of Tyler's head, killing him.