Yes. Either. Does your twelve year old have any musical/technical leaning? My twelve year old son became quite proficient rapidly with PA mixing but he is both a techie type and an excellent sax player, so it wasn't much of a reach. The real problem with training is how are you going to play and teach at the same time? Somebody who knows what they are doing has to be the hands on guidance

Maybe have a talk with the singers about mic technique before the performance. Point out that a setting that gets them heard when they're on the grill will leave them inaudible if they move two inches off.

You won't be the first church to have "kids" run tech. Nothing wrong with that, I don't think, so long as they can keep a clear enough head if something goes pear-shaped.
I know of one who have had a 12yo run video/projection equipment, during VBS and the following few weekends, and another church whose tech team was a 15, a 14 and a 13yo running lights, proPresenter and camera respectively.
Heck, I started audio when I was 17 and by those standards I seem to be old.

If it doesn't cause feedback, you could have everyone back off from the mic a few inches by default. This has less of an effect on volume because the physics of sound means going from 1 inch to 2 inches away causes more loss than going from 2 to 3 inches away.
This won't be the magic bullet but it can help tame it.
As said, mic technique will be the real trick.

Codemonkey, post: 353854 wrote: If it doesn't cause feedback, you could have everyone back off from the mic a few inches by default. This has less of an effect on volume because the physics of sound means going from 1 inch to 2 inches away causes more loss than going from 2 to 3 inches away.
This won't be the magic bullet but it can help tame it.
As said, mic technique will be the real trick.

Right. This is a result of the inverse-square relationship between distance and signal strength. When you double the distance you quarter the signal level. Say you're on the grill and the diaphragm is 1" behind it. If you move back 1" from the grill you've doubled your distance, so your level is 1/4 what it was on the grill, or -6dB. If you start 1" off the grill you have to move 2" back to lose that same 6dB, so changes in position have a smaller effect. But realize that by making 1" off the grill your starting point you have to raise the gain on the mic preamp 6dB compared to the on-the-grill position, so you are starting with more potential for feedback.

Also be aware of proximity effect. At the grill position you'll have a low/low-mid buildup that you'll have to eq out for natural tone. I consider this an advantage as it tends to reduce the effect of plosives, popping "P"s etc.

That's what I was thinking of, in better detail.

But I always thought it was double distance = half the actual volume, which is still -6dB.
Note that 6dB of change in volume does not sound like half because IIRC 10dB of boost is required to "sound like double" because perceived volume and the amount of physical energy change differently.

Also, I'm technically oversimplifying because the mic grill is not right on the part that picks up sound, there's already an inch or so of distance inside the mic. Noone I've ever seen could sing with their lips pressed against the grill.

bouldersound is right, this is far more likely to cause feedback than I give it credit for.
Heck, I found myself onstage at rehearsal tonight using a mic and for the first time, I properly heard the wedge from the singing position. Yikes, that thing is hot. Not I'M GONNA KILL YOUR EARS hot, but enough that it starts to get a little funky in the midrange.

Another thing to think about is how much the singer moves around. If they are constantly moving, it might be better to have someone turning the dials than trying to hack physics.

IMO the fastest fix for the singer will be a headset microphone-wired or wireless. Then the distance to mouth is constant.

Train the singers how to sing. Train the players how to play. This is how it used to be done. Musicians and singers should mix themselves.

Codemonkey, post: 354026 wrote: But I always thought it was double distance = half the actual volume, which is still -6dB.

It's quarter power, which is -6dB SPL. In voltage 2:1 is a 6dB change, but in power 2:1 is a 3dB change.

Thanks for the input, everyone. After playing just this last Sunday, though, I had a bit of an epiphany...

I realized that a big part of our problem is not the FOH sound that the congregation hears, but what we hear over in our performance space. I think I haven't been paying nearly enough attention to good monitoring. For instance, this past Sunday we played outside under an open-sided tent, so I took more care with the monitor setup knowing that there would not be any walls to reflect back the sound from the main speakers for us to hear. And, surprise, surprise, we sounded much better. That's a judgement based on what I, personally, could hear, and on the fact that people in the congregation came up to us afterward and said we'd never sounded better.

Looking back it's a no-brainer: if you wanna sound good, you gotta hear well.

Live and learn.