I'm happy to report that this afternoon I was finally able to watch Le Tour switch both on and off, in fewer than 10 minutes total! This happened Thursday afternoon at 12:55 CST, thanks to a bunch of environmental organisations who called for 5 minutes de répit pour la planète*. The city of Paris agreed to shut off all "unnecessary" lighting, including the Eiffel Tower, for the occasion.
So, at 12:55 CST, I sat in my darkened cube, ready, at the computer, watching the Eiffel Tower, et viola! It went out! For 5 minutes Le Tour, and surrounding area, were dark, with the exception of the news vans parked below. Then, at 1 CST, the Eiffel Tower began to sparkle and was lit!
*Sorry there's no English language article about the "5 minute break for the planet", although I did find mention of it on a couple of forums? I don't know. I guess this is where I drop google.fr and their useful google language tools? *french shrug*