I've made a couple of errors with plastic in the last few months...

If it's catalin or celluloid rather than bakelite be careful that you don't use a polish that leeches out the colour. If you unpin the scales try a spot on the inside first.

The meguiars or 3M lines of clear coat polishes for cars with a clean muslin wheel might work well. If the plastic is tougher the Plastic polishes do a decent job and if the plast is really tough things like blue magic metal polish, simichrome or even brasso do a really nice job. The last two seem best saved for bakelite as I have bleached a few plastics with the metal polish.

You may want to start with soap and water then toothpaste or thin baking soda paste to see how things react.

Go from gentle to aggressive until you find the right formula.

-Bob