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I had the same problem with my Tesla Mobile Connector. At first I replaced the GFCI receptacle with a regular one. Later I installed Tesla’s recommended home charging solution, a Wall Connector.
My E-ZPass would not work when installed to the right of the rear view mirror on the windshield. I moved it to front edge of the glass roof of my Y on the passenger side and it works fine.
You will receive notifications from the Tesla app on your phone as the charge approaching completion and when it completes. I verify that Sentry mode is active before walking away.
Perhaps you can get a USA federal income tax credit for a new panel upgrade.
https://www.energystar.gov/about/federal_tax_credits/non_business_energy_property_tax_credits
I'm so glad that Elon has posted so much about what Full Self Driving will be capable of doing. We can expect him to deliver all the features he promised.