When I was a medic for 15 years, I was paged out to 4 suicides, two self hanging, one OD, and one wrist slashing, (all male). Nor can I remember any reports of suicide by gun either. There were also good number of attempted OD's though. And this was in a rural community where almost every home had at least one gun and often more.

I don't think anyone could prove one way or another why guns didn't seem to be a choice for suicidal people in that community. I certainly don't know. But people who are not of sound mind often do strange things for inscrutable reasons.