It would be "greener" not to light it for an evening. And to remind people to reduce their consumption of things that pollute overall. Obviously not a total solution, but a start.
More generally, these "solutions" don't work. Billions of people don't suddenly all agree to reduce their quality of life voluntarily. For every energy efficient lightbulb there's some beef they aren't supposed to eat, or a standby device that uses 2W too much power they have to switch off and on 5 times a day. It's never happened before and it won't happen for this, even if the world goes to crap due to climate change. Maybe stop wasting resources on feeling good about optimising the uncommon case and work on systematic stuff like clean power.
It has happened that economic growth has untethered itself from fossil fuel growth almost everywhere in the Western world.
I think consumer pressure can do something, apart from anything people just using it as an excuse to save money will do something. I agree that most of it has to be systemic, but there's a combination there. You need for instance cheaper storage and solar, more efficient a.c., better insulation, and so on, but you also need people to want to put in the effort to buy or install it.
Hmm, then why is 67% of US electricity production is from fossil fuels?[1]
The disposal industry already has those solutions, because the error rate in individually-sorted trash is too high to work with. The point of having you sort your own trash is to make sure you're committed to the project, not to save effort for the disposal industry.
I hope you're joking, because that would be mind control on a level not seen since the Wall came down.
Go home, and start burning your household trash in your home woodstove.
All in all, I don't personally have any issues with lighting up the Eiffel Tower if that means a lot of exposure and information about sick planet reaching more people.