My brother found a fledgling about 2 days ago, and only recently(today) did we find out it was one. The only reason we took it in was because we thought it to be a baby. Anyway, disregarding comments such as "bring it to rehab" and "put it back," I'd like to know how I can open its mouth(get it to gape). I tried tapping its head, its nest box, and cupping my hand around it. It still won't gape. I need advice asap since I won't be able to bring it to rehab today or tomorrow and I'm afraid to put it back since our neighbors are constantly mowing their lawns and we haven't seen its parents as we brought it outside.

Have you tried wrapping the bird in a towel when you try to feed. Cold birds won't gape, so this might work.

When I hand raised finches I would put them in a rubbermaid container, on top of a towel, on top of a heating pad. This kept the baby warm and easy to feed.

If this doesn't work let me know and I'll try to find some info for you.

As the baby is a fledgling it may be to afraid to gape, it will be used to its mother feeding it and not know what you want very difficult to overcome this fear in young birds that have been parent reared ,
As said the bird will need to be warm to gape
Also if you touch both sides of the birds beak (you may see a pink yellow or white loose part at the biginning of the beak each side , gently touch those with your fingers this may help stimulate the gape response , if it doesn't work like that add a drop of warm water to your fingers and touch the yellow , white , pink part (will be different color dependent on species ) also keep in a small container so the bird is more comfortable and isn't as stressed,

Getting a fledgling to gape is by far no easy task to undertake, and may take a day or so to get the little feller to gape properly,
Good luck
Katie