I have a two tone RO which does the same thing. It happens because I seldom if ever wear it. Those two tone watches I have (i have 2 others), do not develop this oxidation because they are in heavy rotation.
When that happens I soak it in a bottle of silver cleaning solution (the kind which is meant for use on silver jewellery). It has a sieve tray in a small bottle, meant for holding the jewellery while soaking it in.
I believe the method of using an aluminium foil, baking soda or polident, will work too, because the oxidation comes from the copper content of the Gold alloy. In this method, simply put the watch in a cup, with the oxidised gold area in contact with aluminium foil. Pour warm water and baking soda and some table salt in, and let it rest for 10 min. It will start an electrochemical reaction which removes the oxidation. It is a safer method than using polishing cloths or using silver cleaning solution.
The patina disappears after 10 min. Hope it helps.
I am hesitant to use cape cod polishing cloth on it, because it polishes the metal away.