Another statistic is that gun-owners are statistically more likely to successfully commit suicide. Red States have higher proliferation of guns, and often its easier to obtain a gun.

Modern paramedics can rescue people who take a lot of pills, or do other, less successful forms of suicide. But a bullet-to-the-head is often fatal. No coming back from that.

So it could be a case of "successful" suicides vs "unsuccessful". I'd assume that the rate of "attempted suicides" is roughly equivalent across the country. But an uptick in gun-culture could increase the number of "successful suicides", so to speak.