If you used the gun in self-defense, trigger pull is irrelevant. After all, you're claiming you intended to pull the trigger. If you claim it was accidental, then trigger pull can be very relevant. Of course, the fact you're pointing a loaded gun at someone you claim you did not mean to shoot speaks volumes as well.
One of the worst things to happen is to claim self-defense but then claim you didn't mean to pull the trigger. Entirely inconsistent, but I've seen that more than once.