I dont think that question can be answered meerly with ages, so ...
When I was 10 I went to live with my father to help him out, long story short he had brain surgery at the same time he was going through divorce. I was all he had, he needed me and I stepped up. Over the course of the next couple of years we spent a lot of time learning about gun safety, the do's and do nots, when I was 12 I had full access to every firearm and ammunition in the house. The key here is that I wasn;t curious, I did not have the "wow a gun" factor. That and I was pretty well adjusted shooting and handling. At 12 years old I had my own .22 Remington and 12 guage Mossberg 500. I was home alone for a couple hours on occasion and I dont think my father ever worried about me being able to defend myself in that type of situation. I have to say never did i just play with the guns, I didn't have to, it wasn't the forbidden fruit for me.
With that being said the situation came in handy one night when his ex wife showed up with new boyfriend, arguement commenced and the new boyfriend was holding a gun (not pointed at my father) he was holding it to his side. I was watching the situation and seen this, went to load his .32 revolver and passed it along to him. Another long story short, the new boyfriend decided it was time to leave and did.
The thing with kids, it all depends on the situation, maturity, responsibility. One 14 year old I can trust with a shotgun or any other firearm... another one I may not give a slingshot to.
As far as being home alone...
Lets say you leave your 14 year old home alone and defenseless... BG decides that your house is his next hit.. where does that leave your child?
Personally I am not leaving my child home alone without means to defend himself in this situation, and therefore he will not be left alone until responsible enough to trust with a firearm in the home.
I would not want to live the rest of my life knowing my son would not have been killed in that breakin, if I were home, or he could get to a gun to defend himself.
It is different for each individual, and what they can and cannot be trusted to do.
Hats off to this 14 year old!
I know I am not in Arizona, but the headline to this caught my attention...