If it is real gold- don't use vinegar. That's an acid and gold don't like acid. If it is real gold, treat it like you would gold plated flatware. Gently, with mild detergent like Dawn and warm water, rinse with clean water, and dry before water spots form. Or if it gets really grungy, treat it like gold plated jewelry and use jewelry cleaner, polishing cloths/wadding, or a warm water and mild detergent with a couple drops of ammonia.

Excellent for natural stone and safe for your fixtures: https://mbstonecare.com/mb-5-stone-more/?sku=MB-5QT-S&gclid=Cj0KCQjwv7L6BRDxARIsAGj-34rpyPH6DbCTUQlebWfgT5gJoU0gc6eNV7gjFAEFI68Jm8YTq_xpjXsaAnfWEALw_wcB

If it is real gold....nothing will hurt it! Gold shines bright through sitting on the sea floor for 200 years and when buried in the ground.
But I suspect it's not really gold, but another alloy.
Try a quick wipe with rubbing alcohol. It's not good for the marble but won't etch as quickly as vinegar will. But what about a spray of an all putpose cleaner like 409 or a Method product?