There is a guy on eBay that put up a quick video showing how to clear your lights with acetone liquid as well. He says the acetone reflows the polycarbonate. In both the vapor smoothing and the straight up liquid wipe, the oxidation is always removed with various methods like sanding or machine buffing or 0000 steel wool. Once they have a smooth feel and an even white haze and you have cleaned them with distilled water and dried them off, you saturate a paper towel and lightly wipe them with a slight overlap but never wipe twice. Same concept as "Wipe New" product and some others.
Acetone is used to synthesize methyl methacrylate. It begins with the initial conversion of acetone to acetone cyanohydrin:
(CH3)2CO + HCN → (CH3)2C(OH)CN
In a subsequent step, the nitrile is hydrolyzed to the unsaturated amide, which is esterified:
(CH3)2C(OH)CN + CH3OH → CH2=(CH3)CCO2CH3 + NH3
The third major use of acetone (about 20%) is synthesizing bisphenol A. Bisphenol A is a component of many polymers such as polycarbonates, polyurethanes, and epoxy resins. The synthesis involves the condensation of acetone with phenol:
(CH3)2CO + 2 C6H5OH → (CH3)2C(C6H4OH)2 + H2O
Many millions of kilograms of acetone are consumed in the production of the solvents methyl isobutyl alcohol and methyl isobutyl ketone. These products arise via an initial aldol condensation to give diacetone alcohol.
2 (CH3)2CO → (CH3)2C(OH)CH2C(O)CH3
Now with the vapor method (see 3D printing vapor smoothing as an example) there seems to be acetone (or acetone mixed with water maybe) put into a heated coffee mug with a vent cone on top. As the vapor comes out, it smooths the polycarbonate to a new look again by reflowing it at the surface. This is better than the wipe method since nothing is coming in contact with the lens as it's in a softened state. This softened state becomes hard again once the acetone liquid or vapor has dissipated.
Acetone is used in making the polycarbonate so that's why it works so well. Think of spilling hot grease on the stove and letting it cool. To reactivate it you can spill hot grease on it again and watch it turn clear and re-harden again.
https://www.youtube.com/watch?v=z2ZRKPshPVM Using acetone to reflow headlights.