Once the hole is cut, there should be enough room to reach in, and glue a piece of wood to the sheetrock with Powergrab. If you fumble one inside the wall, and it drops, it won't matter.
Patching over a bracket is the situation in my original post, not patching a hole, but I agree that gluing wood backing to support a patch for a hole is often effective. When the back of the drywall is dusty, sometimes adhesive doesn't stick to it. I've also tried attaching wood backing to the drywall with drywall screws - work's well when you can hold the wood steady while driving in the screws. I've also tried using drywall clips ( https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1 ) and they are effective on drywall that is in good condition. A drawback of clips is that I have to order them. Local stores only sell them in expensive "hole patching kits" that contain only a few clips.
Patching over a bracket is the situation in my original post, not patching a hole, but I agree that gluing wood backing to support a patch for a hole is often effective. When the back of the drywall is dusty, sometimes adhesive doesn't stick to it. I've also tried attaching wood backing to the drywall with drywall screws - work's well when you can hold the wood steady while driving in the screws. I've also tried using drywall clips ( https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1 ) and they are effective on drywall that is in good condition. A drawback of clips is that I have to order them. Local stores only sell them in expensive "hole patching kits" that contain only a few clips.
Also works well for reinforcing the drywall to address your concern. Generous amount of white glue, a 6” length of a painter’s stir stick, couple of office bulldog clips as clamps. It’s like adding a 1.5” x 6” washer behind the drywall. Still thin enough to use the flappers to secure the box, but strong enough to secure a box using its plaster ears and #6 screws if you want.
Comments made here are my own and, according to my children, do not reflect the opinions of any other person... anywhere, anytime.
Up here in the frozen north, steel boxes are still very popular & preferred by most electricians. Steel boxes take a lot more abuse and fewer issues with stripped screw lugs. I seems like in the US plastic boxes are most common. The one place where plastic boxes have the advantage is with sealing in exterior walls. I've used both & personally much prefer the steel boxes.
The 2104 is a 2" x 3" welded box that is excellent for use in old work. They can easily be screwed to a stud through the side. If no stud is in the desired location, I glue a short length of 2x2 to the back of the drywall & secure the box to it. The nice thing about the 2104 is that it only needs a 2" x 3" hole, with leaves a large safety margin for sloppy cutting or torn paper. Less patching with them.