Noel, that's for getting rid of the yellow patina on white plastic. I can't say for certain, but it kind of feels like those techniques wouldn't work on clear plastic, (which is oxidation and UV discolouring of the protective film over the polycarbonate).
The only effective remedy I have ever used is progressively finer sanding, followed by polish and a UV protectorant.
You can use fuming acetone to reflow the polycarbonate, (acetone is the solvent used to produce poly in the first place) but it's properly risky and can end up making it extremely brittle. Which is to say that a stone chip that your light might normally shrug off instead causes it to freaking
explode.
::edit:: Here's a dude reflowing the poly
with liquid acetone.
A couple of notes:
1) If you choose to try this, make only one pass. Otherwise the towel will drag and you'll end up with ridges.
2) For pity's sake, take the time to remove the light cluster from the car. Don't risk your paintwork, especially with 0000-grade wire wool!
3) "Blue Juice", as he calls the window cleaner, is the vetenarian's phrase for pentobarbital. It's what they use to put animals down. I have never heard anyone call Windex/Windolene that.