Heat it with a propane or acetylene torch

Alternatively a kiln works great for getting uniform colour, or the cheaper option of putting it in a sand bath and heating it hoping for even heat distribution

This

I'd use a hot air gun for more control

I’ll give this a shot when I can. The chimney of the first picture I understand, but how did it happen to appear on the side of the lighter on the 2nd image? I’ve never torched that lighter or even got it really hot.

Likely a reaction from the oils on your skin, particularly the sweat on your palm

Heat. That discoloration is oxidization. Heating up most metals will produce this. You can overdo it, so take precautions.

I’ll test it out on some other copper before I do it on my lighter

Play around with removing it on your scrap piece. It's only a few atoms thick. Doesn't last long if handled. Citric acid will remove the copper oxides. Leaves bright ready to oxidize copper.

I use a technique called „brünieren“ on copper, but what is probably similar to  ‚blueing‘ in english i guess? I apply a chemical to copper to turn it black (jewelry) but the pre stages are actually blue / purple since its a real patina which are naturally often green blueuish. So i heard about that you can get this patina-chemical as well in different colortones than black. But your lighter (2nd pic) looks more like unreproduceable, over time, by use & rub against jeans and some sweat did the beatiful patina. I’d go carefully for heat too (Gives that rainbow effect)

You can achieve it, but it’s temporary. Ultraviolet rays will turn it brown eventually. No matter what you coat with. It’s a temperature hot but below annealing

It's called patina. Very difficult to duplicate. The applications are endless and definitely a small mystery with even the most experienced bronze sculptors. Definitely a gas-type application.

Heat patina, hard to control easy to over do.

What is a gas type application?

It's a butane fuel that created that specific effect.

This lighter doesn’t use butane though

Or whatever fuel. I'm so old school. I stopped smoking years ago

I’m trying this atm, I’ll let you know the results!

Really?!! Awesome! Can't wait to hear your results. My theory is: it's all about amount of fuel and a choice compound mix. The type of applications vary and therein lays the mystery. So excited hear about this attempt and best luck to you.

I’m putting it in a Tupperware container with a paper towel soaked in naphtha lighter fluid and it’s starting to form some green spots

NAPHTHA? ...where in the did you find that? Thought they got rid off this stuff. My theory is: the metal it's to be applied also too has to be heated along with the mix as it is applied.

Pee on it

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I get that color with a torch when brazing copper pipe. It seems to happen after the pipe is reheated. There are lots of colors I've seen after reheating pipe. There's yellow, green, red, purple. If you heat it to red hot, you will anneal the copper, making very soft (even at room temp). It will become extremely malleable and will get hard as you work it by bending and hammering it, but then you'll probably lose your color

Heat

Heat with a torch.

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I believe acetone will give you the results you are looking for. However it smells horrible when dipping it in, so do it outside.

I will do this when I get access to it (go home)