I have used Rustoleum spray or RubNBuff before to refinish different decor items and lighting, but the fact that it is a transverse rod will make it much harder and you won't be able to just spray it without very carefully taping off the moveable parts.

Maybe just try toning down the gold shine and don't try to go all the way to oil rubbed bronze.

I'm not familiar with RubNBuff - is that what you'd recommend?

buy a new one. painting may have a negative impact on moving parts.