The picture is not important. I have done more google searching and came up with a few things to try. I will have my electrician friend help me check that I don't have hot and neutral reversed at the pump. He may have a megger (and know how to us it) which is a supposed to be a very useful test device for these situations. I will replace the non GFI receptacle with a new one in case it got corroded . I will replace the one receptacle cover that is worn and not sealing correctly any more. Then I will see how it goes.
I also learned that when the gfi trips, pressing the test button first resets it completely. then press the reset button.