So I have a hole in this drywall. What happened was water was leaking from the vent shown in the photos below, which probably caused some rotting of the wood, although it's hard to say exactly what happened because some type of animal was also living in that same area, you can see a few eggs in the far left corner of the photo.
So anyway, I'm trying to figure out how to fix it. My best guess is to either run a new piece of wood parallel to the damaged one, and then a couple of pieces of wood perpendicular to the one that has rotted out a bit, those would be to secure the new drywall after I cut out the section with the hole. That's what the blue lines represent in the photo. I don't know if I'd need to run a whole new piece parallel to the rotted one, or just shorter piece nailed to it, or leave it as is. I'd have to check again to see how bad the damage is, but there is some as is obvious in the photo.
What other options do I have, especially anything easier because the crawl space above the ceiling is fairly small. I guess I could also cut out a square around the hole, put a piece of wood in it going across the hole, screw it in on the sides, and put the new piece in (Shown below).