Car wax
First thing i would try on it is buffing compound sold at auto stores, walmart etc. about any system uses abrasives to get off the oxidized layer, your gel coat is from 1 to 10 mils thick. so if mild abrasive (buffing compound) keep working your way up the scale, with sanding being the last. Caution though if you sand too much, you can sand through the gelcoat, then painting is necessary.or if you dont want to use abrasives you can put baby oil on it every 3 days. Seen people do this to make a quick dirty sell.