Update August 8, 2019 - 5:30pm EST - It finally came down to the ECU/throttle body. The scooter would start when I would tap the ECU. A Modern Vespa Forum poster surmised that it was poorly soldered pins in the ECU/Throttle body. The problem got worse and I decided tapping the ECU every time I wanted to ride wasn't the best solution. So, my wife and I replaced the ECU/Throttle body. In doing so, I think we broke the fuel injector electrical connection - I blame her . So I replaced the fuel injector. The bike still would not start. So I tried to do a TPS reset using JPDiag (an online ECU code reader). I'm not sure the TPS reset worked - I did email the developer, but I think he/she is in France. I'm waiting for a reply. The ECU is returning error code P0611 : invalid signal. The scooter's attempts to start look like this: https://youtu.be/xShccopJEm8
Anyway, I don't have access to the Piaggio PADS diagnostic tool to do the factory-authorized TPS reset. I'm giving up... I'm going to bring the scooter to the local dealer. It will be the third mechanic I've been to... Hopefully three times is a charm.