The area I think you speak of Big Saw would be down in the throat latch area. Basically where the head attaches to the body on the belly side of the fish. Debra Johanssen use to show how to do this on her show with Kevin Geary years ago. Basically allowing the fish to dangle straight down via gravity and grabbing ahold up under the gills and using your two fingers extended (or thumb and other fingers and grab for big fish) around the throat latch to keep the fish from falling if it were to flop. Helping support the weight with your other hand down before or aft the anal fin.
I know you all know this, but just so there's something in the archives that uses the proper terminology so newbies understand. Avoiding the gills at all costs and avoiding putting the weight on the gill "cover" (I'm guessing gill plate is a slang for cover? I've always heard it called the operculum. That's the bone not the gill cover...)