I think the following quote best illustrates Jerry's impatience.
“I want some swimming goggles,” he panted, defiant and beseeching. She gave him a patient, inquisitive look as she said casually, “Well, of course, darling.” But now, now, now! He must have them this minute, and no other time. He nagged and pestered until she went with him to a shop. As soon as she had bought the goggles, he grabbed them from her hand as if she were going to claim them for herself, and was off, running down the steep path to the bay.
Jerry doesn't ask his mom if she would be willing to buy some goggles. He doesn't ask if it would be okay. He doesn't even explain why he needs/wants a pair of goggles. Jerry simply announces that he wants them. No "please." Knowing my wife, my kids wouldn't be getting the goggles, if that's how they asked. Additionally, the quote has the impatient "now, now, now!" section that is quickly followed by the words "nagged and pestered." Jerry is incapable of waiting. Then, after he gets the goggles, he grabs them and takes off running. Not walking.
The next quote that I think clearly shows Jerry's impatience is this one:
He did not ask for permission, on the following day, to go to his beach. He went, before his mother could consider the complicated rights and wrongs of the matter.
Jerry is entirely focused on himself. He isn't willing to ask permission to go. He's not even willing to wait until his mom wakes up, so that he could perhaps tell her where he is going. Nope. Instead he just gets up and goes. No waiting involved.