How to use acetone vapour to clear headlights?

Answer: Don't.

Never heard of it. Sounds suspicious. Video you provided is unconvincing, and doesn't look like actual "oxidation". Faded headlights are physically worn, and require sanding and polishing to restore. A volatile chemical blown across the surface is not going to fix them.

Plus, acetone eats certain types of plastic. And its vapors are very flammable.

Toss aside all the acetone equipment and buy a $25 headlight restoration kit that includes sandpaper, polisher and some abrasive/polishing compound and get a drill or get some elbow grease going.

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.

Chemical intermediate

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%)[13] 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.[14]

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.

The heated coffee cup with what appears to be either a hard plastic or silicone funnel to fit snugly over the cup allows acetone vapors to flow out in a small circle about two inches in diameter. https://youtu.be/iOdVqsPcqog

I was sceptical at first as I didn't know if this was a large heated cup creating a dangerous explosive vapor but apparently it's a low heat set-up. While I did not buy this product I improvised with a poly gauze pad as wetted applicator. After going thru the method of progressive sanding papers until satisfied, I wetted a fresh gauze pad with acetone wearing disposable gloves then applied in one single wipe a small area then wiping another area in the same horizontal direction, careful of over lapping. The wet acetone reacts immediately and clears the fogged lens. If applied a second time over the same area, it can cloud the lens. The gauze pad is applied and removes bits of lens material as it dries white on white on the pad. One pad per headlight lens. Since acetone dissolves polyacrylate, the wet application paints it on.

My guess is using an airbrush may be another alternative with low air pressure and zero contact with headlights similar to the heated cup method with a small diameter funnel to flow vapors onto the lens.