How shiny or bright aluminium shines after polishing depends on the aluminium. For comparison, compare the brake backing plate with the side panel I made from 1.7mm aluminium sheet. I've no idea what grade the aluminium is, but as you can see the brake backing plate is brighter than the aluminium sheet. Also compare the fork leg with the ignition switch plate which was made from 3mm sheet, again, no idea what grade the aluminium is, but again you can see the fork leg is quite a bit brighter.
Cast aluminium seems to be brighter that aluminium available in sheet form when polished. What's not shown however, if you look close enough you can see imperfections in the cast aluminium, no doubt due to the oxides accumulated over 46 odd years which appear to have permeated the metal. The sheet material, whilst oxidised when I bought it was not 46years old, a good enough reason to keep the oxide away from the cast aluminium.
All the samples received the same polishing regimen: Sisal wheel with black compound, sewn cloth wheel with white compound and loose cloth wheel with green compound.. Whilst white compound gives a nice bright shine, it is still quite an aggressive polish, so if you look close you can see direction marks made by the angle at which the substrate material is introduced and moved in relation to the wheel. Green compound acts similarly but the direction marks are not as pronounced as the compound is finer in structure. I use a wire brush on the wheels before changing compounds, this removes most of the previous compound whist also softening the fibres in the wheel by stripping and tearing them.
My fingers don't handle wet and dry very well, so I generally use a random orbital sander with 240 grit, or finer, if the surface needs flattening.
If not, I prefer to use a nylon fibre wheel. Nylon fibre wheels are not Scotch Brite, they are considerably denser and harder and available in different grits as well as different sizes and for different applications: Drills, angle grinders and bench grinders.
Nylon fibre wheels are excellent for reshaping and smoothing ports. Inlet ports generally have lumps, bumps and divets along their length. The wheels make very short work of the irregularities, but don't leave a polished surface which fuel can stick to. Pictured are a number of different wheels, 2" x 8", 1" x 8", a 4" angle grinder wheel and some smaller wheels for use with a drill. Just a word of caution when using nylon fibre wheels they can remove a surprising amount of material surprisingly quickly, so you need to watch what you are doing. The wheels can be shaped to get into corners and other difficult shapes.
I use Silvo as a final polish. Gun cleaning cloth is very good to use as a final polishing cloth, but I can't get a hold of that anymore since I departed defence, so now I use Chux. Not the best as it does scratch the aluminium, but everything will scratch it anyway. The difference between a flawless polished aluminium finish and a not so flawless finish is about one minute of handling the aluminium.
PPG paints can supply an additive for their two pack clear which is advertised as providing a better grip on glass, so presumably would do the same for polished aluminium. Something worth trying.
Another option is bright dipping, if you can find an anodiser who knows the process. Not recommended for backyard DIYers as the chemicals involved are toxic. This procedure is used on aluminium to provide an extremely shiny surface for reflectors in torches.