The activist group Americans for Responsible Solutions, founded by a Congresswoman who was shot by a criminal, says they want to enact waiting periods, for example. Those already exist. They advocate for Smart Gun technology, which sounds great. But it doesn't work. iPhone X users are about to learn how poorly supposedly Smart technology works. It's why no police union will ever allow them on their guns. When Smart Technology fails, as it does 25 percent of the time, and a homeowner is shot by a criminal, activists will claim gun ownership does not prevent harm.
Safe storage is obvious but that can't be mandated, and since most suicides are by owners of guns nothing about storage will prevent access. And finally, a serious concern: Forcing doctors to be anti-gun activists. Like a pediatrician who says they won't treat a child if the parent is anti-vaccine, forcing doctors to quiz patients about guns is going to be abrasive and that will lead to patients finding new doctors. It also forces doctors to engage in behavior that is outside their legal jurisdiction, no differently than if they ask patients if they go to church or read a newspaper.
The group doesn't discuss the real culprit: mental illness. Instead, they posit that a despondent person who has access to a gun will not fail in a suicide attempt whereas with a pill they might. Except we know that isn't true. Guns are banned in Japan but suicide did not go down at all. They commit suicide by rope and have incredible success at it.
In reality, people who commit suicide using something like a pill may be issuing a cry for attention. People who shoot or hang themselves mean to kill themselves.