Stricter gun control laws should imply less access. One of the nordic countries may be an exception off the top of my head, as one of them has strict gun control laws but many people still own a gun. Finland, maybe? That absolutely needs more research by me so take that with a grain of salt.

(I am going to clearly re-emphasize "spot check" here, as well.)

If countries like Japan and South Korea had lower numbers of suicides, that may indicate that gun laws play a part in that. (Japan was the exact reason I added a disclaimer about cultural views affecting suicide. Their history with ritual suicide is interesting but probably doesn't carry over much to today. )

Comparing any other countries total suicide rates to to that of the U.S. was a fairly quick search. My searches gave results for the years between 2020 and 2022 usually. There were a ton of different results, but I could say that a "decent" world average is about 15 in 100,000. If I remember correctly, I saw everything between 10-25 deaths per 100k, maybe more or less.

The U.S. averaged around 18'ish per 100k, which seems a hair higher, but not outrageously high.

If there was a direct correlation between firearm access and suicide, it should create a hell of an outlier for U.S. suicides in total. Also, I did read a few studies on preferred methods of suicide based on gender and also suicide methods in general but that was irrelevant to the topic. (I was looking to see if access to guns increases suicide rates not if access to guns influenced the preferred method of suicide.)

For a quick glance, that should be sufficient.