I am missing Switzerland there.
By law, every Swiss male, adult citizen has to have a gun in his house for purpose of being ready for war.
That makes also Switzerland the country with largest gun suicide rate.
US was second in gun suicide rate, but overall the US suicide rate is not that big.
In summary, having an availability of gun make gun a preferable choice for person who decided to kill himself.
If there is not gun around, that person uses different tools.
Taking away the guns will not change the suicide rate at all!
Also, Japan has a very high suicide rate, higher than that of the US, but also has very strict gun control laws (it’s basically illegal for a civilian to own a gun there).