Welcome to the forum John There has been a few previous threads on this subject. Some take them off and use a polishing mop on a grinder spindle. Some use a Dremel or similar hand tool. Some use old fashioned elbow grease. Autosol chrome cleaner is good, depending on how bad they are you may have to go back to fine wet or dry paper. Personally I would not remove them just for polishing, unless I had to strip the engine for some other reason.
Are the cases just bare alloy or do they have a clear-coat on them? Until that is established I wouldn't do anything abrasive with them, just soapy washing.
I was told by my dealer that they are bare alloy. I use a Scotchbrite pad and follow the lines of the existing brushed finish. Comes up a treat and a lot easier than trying to polish them.
I use Peek as it's not as abrasive as Autosol and leaves it looking factory finish. My dealer suggest Autosol was also a bit harsh for the Chrome as environmental processes mean it's not so durable as 'the old days'. FS365 applied and excess wiped off keeps them good in the winter.
They come in various grades but they are only plastic so even the most coarse grade isn't so aggressive. You just need to lightly buff across the surface until you get the same brushed effect. Clean any dirt in the usual manner then start light and get progressively firmer until you get the right finish. If you mess up you can always autosol it back to a smooth finish and then start again with the scotchbright.
I know a guy who used Solvol Autosol on his T120 and it looks great - not sure how often he needs to re polish though. Last Sunday at Sammy Millers I saw a black ( black tank with chrome pipes/wheels - not the Black with brown seat !) T120 that had been polished and it looked great. Unfortunately , I could n't find the owner to ask what he used which is a pity because he also had numerous aftermarket stuff on it - Remus slip ons, bar risers , very nice looking small bar end mirrors, etc. I wanted to ask about it and listen to those pipes but no way of getting hold of him as there were hundreds of people there. Perhaps if he/she reads this we could be told?
I do just the same as Murdo. Ive been using a mild PH soap and hot water solution to clean the bare Alu, too aggressive a cleaner can mark/stain the Alu. Use a scotch bright pad if necessary (going along the grain, then protect with ACF-50. (wiped on, not sprayed.
Mines a Thruxton but the same applies. Did not care for the brushed look so simply attacked them with elbow grease and Autosol, then Autosol Aluminium polish which seems a bit 'milder'. After polishing with metal polish I give them a rub with Pledge furniture polish, the aerosol lemon flavoured stuff.