Here in Ireland guns aren’t readily available, but nor are they illegal*. In general if someone want’s or needs a gun they can apply for a licence and most of the time that application will be granted.
The application process is complicated enough to deter casual gun ownership. You need a licence for each gun you hold which is bureaucratic and has cost implications which is probably enough to deter ownership of lots of guns.
The application is made at your local police (Garda)**station, and a senior cop will decide if the application should be granted or denied.
There is a part of the application form which must be filled out by your doctor stating any mental or physical health problems that might impact on your ability to own a firearm safely. The senior cop will make a decision based on this.
So ‘Mentally Ill’ isn’t black or white nor does it have to be.
The gun laws here are more robust than most countries. This is almost certainly an artifact of being occupied by the British up 'til about a century ago. The war of independence and the subsequent civil war certainly didn’t help. Nor did the troubles of about 50 years ago. Historically, the Irish Government has been afraid of guns.
*Not all guns are legal and not all ammunition is legal. Sub-machine guns and assault riffles and military ammunition is flat-out illegal. Handguns are extremely restricted.
**The cops here still police by consent. I’m not suggesting they’re perfect, but they generally have the trust of the populace.
I’m not for one minute suggesting that the US’ gun problem can be solved by simply licencing guns. The problem is too big and too complex for such a simple solution. But it’s a no-brainer that certain individuals shouldn’t be allowed access to firearms and in Ireland, the gate-keeping is done by licencing.
There is relatively little gun violence here. And most of that violence is committed with unlicensed/illegal firearms by criminal gangs.
Interestingly, there are reckoned to be tens of thousands of unregistered firearms hanging around from the conflicts of about a century back.
If you’re interested, the gun licence application form is here…