There are so many other factors that contribute to suicide (culture, socioeconomics, age distribution, and another bunch that aren’t even on my radar) that might be more significant than gun prevalence. Heck, even in countries with similar gun prevalence I’m sure the breakdown for elected methods of suicide likely differ due to these other factors.
You’re likely correct, access to guns is by far not the factor most highly correlated with suicides, if perhaps strongly correlated with method of choice.
I came across this disturbing statistic from worldpopulationreview.com
Suicide in South Korea
According to the World Health Organization, the suicide rate in South Korea is the fourth highest in the world. One factor in its high suicide rate is suicides among the elderly. Traditionally, children have been expected to care for their aging parents; however, because this system has mostly disappeared in the twenty-first century, many older adults commit suicide, rather than feel like they are a financial burden on their families. In addition to the elderly, students have higher-than-average suicide rates, at least partly because they feel high levels of pressure to succeed academically. When they do not achieve their goals, they may feel that they have dishonored their families. Alcohol use, sleep deprivation, stress, and poor social relationships can put students at increased risk of suicide.
One of the most common methods of committing suicide in South Korea is poisoning via carbon monoxide. Additionally, many choose to jump off a bridge. In Seoul, the Mapo Bridge has earned the nickname "The Bridge of Death" or "Suicide Bridge" because of how many people jump off it. The government of South Korea is making efforts to curb the suicide epidemic. It strives to increase mental healthcare access, a necessity as 90% of suicide victims in South Korea may have a diagnosable and treatable mental health condition. It is also providing education to community leaders to help prevent suicides at a local level.