....shutting ones mouth is the best applicable action. We have a right to do so granted to us by our laws.
It's a very important right. How and when to exercise it is the question.
If somone has killed a neighbor or relative, you should say
nothing without the advice of counsel.
If someone has taken all of the money out of the safe where you work, you should say
nothing without the advice of counsel.
If your organization is under investigation for conspiracy to defraud, you should say
nothing without the advice of counsel.
...and so on....
But--if you have shot someone in your house, and there is an accomplice with a gun still in your house, does anyone really think that shutting one's mouth is the best applicable action? That one should be obvious.
If someone has held up the bank from which you had just come and you can describe the getaway car, should you remain silent?
The self defense case differs from almost all other kinds of cases. You will have to admit to having willfully used deadly force, and you will have to present evidence to the effect that you were justified. The gathering and securing of that evidence is not something that you can do--it is beyond your control. If the police at the scene miss it, you won't be able to use it. If they have no inkling that the shooting involved self defense on your part, and if all indications point to a criminal act on your part, they won't be looking for evidence indicating that your use of deadly force was justified. They might see it and recognize it and they might not; and time is of the essence.
That's discussed in some detail in
Lessons from Armed America. That book has received high acclaim from the recognized experts on this and other fora. If anyone who has read it would like to present an opposing view from a supported, objective, and reasoned standpoint, I'm sure that everyone here would appreciate it.
You should
of course say
nothing about the details of what happened until you have the benefit of the advice of counsel. However, if you can do anything at the outset to keep an obvious homicide on your part from rapidly turning into an otherwise unstoppable criminal prosecution that could cost you your fortune, your record, and your personal freedom, it would probably be wise to do so, in my humble opinion.
Mas Ayoob's approach, which is the same as that recommended by Fiddletown and by Kathy Jackson and which is very close to that recommended by Marty Hayes, is intended to do that. All of them have explained how failing to do so could prove very harmful to you.
You do have a constitutional right to not do so, of course....