To me just looking at the gun rate of countries and the data it seems that high gun ownership definitely correlates to increased suicides and a moderate to low overall rate of all gun deaths, but it also seems that the highest ownership of guns seems to stymie a higher murder rate, although Swiss is an outlier, where its even lower, but their suicide rate makes up 85% or more of their overall rate and culturally Europe seems to have a low overall rate, probably since the french revo and all.
Latin america and most of africa seem to be exactly opposite of high ownership countries, they have extremely low rates of ownership and most have anywhere from 2-6x the overall murder rate of the US and have minmal suicide rates and high rates of gun homicide, almost exclusively most of the overall gun death rate. Venezeula has free healthcare and 59 deaths/100,000, so thats probably a good thing, high rates in virtually all of Central and South America and non Arabic part of Africa, stats wise.
Chile is an obvious exception, however they dont grow cocao and the Andes and the sea provide historical natural barriers. All of the North African states have oil. Are they correlations, maybe, maybe not.
The pacific rim opposite of us has moderate rates, the Phillipines is similar to US in overall rate, but they have a 10,000 of 1% of the amount of gun ownership that the US has...
Also multi ethnic societies seem to dominate the high rate of ownership/moderate to low amounts of gun death rates.
Who has a state by state breakdown