I think most mass killers have mental issues. They do not include health into background checks (violates HIPAA law if they do). Most liberals want to include health background check into the process which I agree with. Problem is... you can always find a doctor that will clear you. Would doctors want this additional responsibility? It opens a whole new can of worms.
When I buy my gun, I'd have to fill out applicate wyth my SSN, address, DOB and etc. Dude would call government background check agency and they would run an automated background check on me that takes 1-2 minutes. If I have anything criminal or pending, I would automatically get flagged. The background check agency would give clerk authorization code that background check was completed and he would proceed with a sale.
Mental or behavioral health can be added to the background check without violating HIPAA, much the same way it is done for other background investigations.
--thinking back to my security clearance process in the military. they ask if you've sought help for mental health, who you saw, when you saw them, and their contact information. they do not ask for diagnoses, but just ask the provider if you are capable of the task.