Training and equipping watchstanders with firearms is the easy part.
The hard part is that the shooting at PHNSY is one of about a half-dozen incidents in the last year (that I've heard of, which means there are more) where an American armed watchstander used his duty weapon to inflict harm upon himself or others around him. The Pensacola incident is getting more media attention because of the terrorism narrative, but the ratio of foreign terrorists vs. mentally unstable Americans shooting people on military bases is very small. The policy makers are looking at this data.
The common thread among the slew of active shooter incidents going back to Fort Hood in 2009 is they are committed by someone who is A) authorized access to the base and B) usually authorized to carry firearms, even if he doesn't use his duty weapon to commit the act.
We need a more robust screening process for issuing weapons. We have to get that part right before we expand the number of people we arm.
It would be interesting to see if the people involved in the incidents had rec'd a waiver for past psychological issues, of course that probably isn't something that would be released.
I do think a better screening process would be good as well as regular updates to make sure a persons life isn't collapsing around them.
There is also the leadership part, a good leader knows his people, and tries to know what is going on in their lives. I have had a few shitty leaders (CPO's to senior officers) and they can make your life hell, I have seen people break that I never thought would, it was during those shitty leaders that I saw more sailors talk about hurting themselves than any other time. In each case the persons reputation had preceded them as being bad to their people. The USN is quick to discard a good officer who damages a ship, but a shitty officer who destroys lives, it can take years for them to get shit canned, if at all.
I am also not about coddling sailors, if they mess up they get punished, set the standard, make sure they have what they need to get there and hold them accountable.