Any legislation relating to mental illness does nothing but create a subclass with less rights. You can either be honest and argue for full restriction of firearms or nothing. I had problems with depression in my early 20s, am I too mentally ill? All a law like this would do is incentivize people to never get help, never see a doctor, and never get medication. The mentally ill don't commit most gun violence. Most mass shooters are not mentally ill, that is a comfortable lie repeated mindlessly by scared people. They're just murderers.
People who just want to take rights away from the sick because they demonize them are literally going to make things worse.