Okay, sounds good on paper - but how does one do that? FBI background already checks:
18 USC § 922(g) & (n). Punishable by up to 10 years imprisonment. May receive minimum sentence of 15 years without parole if offender has three or more prior convictions for a felony crime of violence (e.g. burglary, robbery, assault, possession of offensive weapons) and/or drug trafficking felony.
A. Possession or receipt of a firearm or ammunition;
B. By a subject who falls within one of the following categories:
Felon - (Additionally, persons awaiting trial on felony charges are prohibited from receiving firearms.);
Drug user or addict - (Often shown where paraphernalia seized, subject tests positive for drugs and/or subject claims drugs were possessed for personal use.);
Alien - (Includes illegal aliens and aliens lawfully admitted under non-immigrant visas, i.e., those aliens not admitted for permanent residence. This provision does not prohibit aliens who lawfully possess a so-called “green card” from possessing guns or ammunition.);
Is subject to a domestic restraining order - (The order must prohibit contact with an intimate partner, or child of the subject, and must have been issued only after a hearing of which the subject was notified and at which the subject had an opportunity to participate. The order must also find the subject poses a threat to the physical safety of the intimate partner or child or must prohibit the use, threatened use or attempted use of physical force.);
Has a prior conviction for domestic assault - (Includes a prior conviction for any assault or threatened use of a deadly weapon against a present or former spouse or partner or child or guardian of any such person. The subject must have been entitled to a jury trial and been represented by counsel in the prior proceeding or be shown to have waived those rights.);
Fugitive from justice - (Fled any state to avoid being prosecuted or to avoid testifying in any criminal proceeding.);
Dishonorably discharged from the military
Also, how does one know someone has a “mental illness”?
https://www.justice.gov/sites/default/files/usao-ut/legacy/2013/06/03/guncard.pdf