What does their behavior indicate about them?

There is a sense in which Act III exposes a number of characters for who they really are. Not only has the illusion of Eliza been somewhat punctured by her use of her common tongue to narrate the story of her aunt's experience of influenza, but also we see that Pickering and Higgins are shown to be nothing more than excitable children with their new toy that they are really pleased with. They get carried away with their own enthusiasm forcing even the formidable Mrs. Higgins to have to shut them up and keep them quiet. Any sense of their being credible men of science conducting an experiment of value is lost in the cacophony of their joint voices. Mrs. Higgins treats them like little over-enthusiastic children, and the play shows that this is precisely what they are. Mrs. Higgins of course is able to put her finger on the real issue, which is "what is to be done with her afterwards." She is able to see the long-term impact of what her son and Pickering have done in a way that they are blind to.