How can I make a faux gold finish less garish?
I assume the look you're hoping for is a little like this, a dirty gold:


source, actually a 3d render

If you're not planning on rebending the stand a lot, I'd suggest taking some acrylic paint (maybe some raw umber and black or similar dark and muddy colour), mix it with a little chalk or plaster (gypsum) to make it more dirty and matte (but make sure it doesn't dry out too quickly - you can add a little water while you mix), take a piece of cloth, dip it into the mixture, and rub it unto the lamp.
This way, all crevices will take the paint, and all larger smooth surfaces will be wiped clean again by the cloth.

As a side note: I don't really see the 'gold' in the lamp, only a very subtle, almost green hue. Is it the lighting, the colour profile, or is it really that faint?

Depending on how clear the 'gold' is on the lamp, you can first coat it with some acrylic gold paint, using either spray paint, or acrylic, after you've sanded it with very fine sandpaper.  

Regular acrylic gold paint is usually too cool or too warm,  and too shiny (or, rather, glittery). There are more professional paints available, but you can of course also create your own mixture (white, yellow, and if you're so inclined, maybe warm it up with a very little bit of red).

In both cases, parts of the coating might come off afterwards (especially with acrylics), but this could actually increase the faux antique look.