I can reach inside the guitar and rub the cloth patch in place, "ironing" it down, and even sliding it into position if I need to:
As the patch cools and the glue starts to gel, it "sucks down" to the wood and clings nicely.
A few minutes later when the patch is fully cooled and the glue gelled, I can dab the excess glue off the patch and surrounding area with a cloth and warm water:
Naturally it's hard to reach way down inside some areas, so there I'll use bits of rag held in a hemostat to clean up the area:
After things dry out, the cloth patch looks pretty good.
There's still a little smear of glue and dust discoloring the side, and I can wash that down again more vigorously, or even sand it lightly if I want to.
The hide glue dries quite rigidly and makes the cloth patch an effective stiffening reinforcement for many situations. Best of all, this is a reversible procedure because the patch can be removed by carefully applying warm water, so future repairs are not compromised.