My black plastic side panels are scratched.
I’ve sanded (ending up with 1200 grit) and then tried various compounds on a cloth to polish them up (t-cut, metal polish and brasso - in the uk).
one of those compounds usually works when I’m polishing plastic. I’m beginning to think that these side panels (which are original) are a different type of plastic that I’m used to and maybe a different technique is required? I'm only polishing by hand. I haven't got a buffing wheel. 
Has anyone tried to polish their side panels with success? What’s your method please???
Thanks….
btw, I know you can buy repros of these…
 

I'm not sure if this will be helpful but those covers might have had a "matte" finish rather than "polished"?

Generally if Yamaha had glossy finishes on plastics they were painted.

edit - sorry MarkT - I missed your post there…
except for where the scratches are, the panels are all a polished finish. They do seem to be the original ones. They have got some scratches on them. I have sanded the main flat surface on one. It’s now a matte finish (but no scratches!). Spraying them may be the way forward with these, but they are pretty flexible, so can see the paint peeling off quite easily….
I bought a cheap buffing wheel to fit into the drill. It came with two soaps (but no instructions).
First of all, I used no soap (I watched a chap on you tube where he buffed his plastic mudguards to a mirror finish without using soap) - but nothing much happened.
I then used the green soap - I got a slightly shiny finish on the plastic, but what I want is the factory polished finish….

Got it. Most of the older bikes around here have been pretty sunbaked and I really don't remember what they were like new. I thought they were matte finish.

I also know an old trick we use here in the US to give plastic a "polished" look is to apply a few coats of a multi-surface floor cleaner/polish product called "Mop and Glo"... I'm sure there's something similar in the UK?

Great idea MarkT never heard of that learned something new today