Accidental deaths by gun should be included with suicide by gun, as should homicides by gun attributable to intimate partner and domestic violence (which is the overwhelming majority of homicides for children and women), as these are the gun deaths that are readily avoidable by keeping guns out of the home.
Of course, you would rather take your chances with those, and you are hardly the only one. Most people, especially those who like guns, think that they will be the exception to the clear statistical patterns and that "those things will never happen to me."
Choosing to take your chances with the risk of dying by gun-related suicide, accident, or domestic violence, relative to the chance of being shot by a criminal, is just not logical or rational based on the data. It's a similar psychological bias (with a bit of the Lake Wobegon effect thrown in for good measure) that leads to the media focusing on mass shootings, terrorism, shark attacks, etc., relative to all the other things that pose a much greater risk. That irrational engagement with relative risk was what I thought you were pointing out in your initial response to me.
The research findings are clear and unequivocal: the number one action that you can take to protect yourself and your family from death by gunshot is to keep guns out of your home.