If someone pulls a gun on you and you feel they are a threat to your life then yes you can usually shoot someone for pulling the gun on you.
That is if you are unable to get away from the threat to avoid being shot should they pull the trigger on the gun.
You have a duty to retreat so if you can get away from the threat of the gun without shooting the person then that should be your first option.
However if the person pulls the gun on you and says they are gonna shoot you then you should keep your gun on them in case they decide to pull the trigger but try to get away from the threat first.
You always have to prove in court that you had no other choice but to shoot the person in self defense.
Now if there is no way to retreat and someone pulls a gun on you and moves their finger to the trigger of the gun then you can most always shoot the person in self defense.
But only shoot the person to remove the threat and don't continue shooting the person after they are down unless they try to shoot you again.