A few thing are actually left out.
I understand that you have meant well with the video.
However. some questions are not addressed and that is a concern, as people will watch this and actually believe it is a "answer to every such concern".
Like what is the substrate of the plastic you removed "the wax" from.
What was the solvent system of the "wax", etc, etc.
Just the solvent/carrier system of a "wax/sealant" may actually attack the trim substrate, depending on what that may be and "permently" discolor the trim part.
No amount of use of a brush or any all purpose cleaner is capable of replacing the pigment of the part by cleaning of it.
I could go on and on, but reality it what vehicle, what age of the vehicle, was it from such as an ABS or polyethane based trim, etc, etc etc.
For an example, are you aware that some manufacturers use grill parts that are actually "painted" with a modern "lacquer" based coating?
As far as the "special' brush, well that is a matter, in reality of a "tooth brush", want a stiff one, use a new one, for a softer one, use the one that you replaced with the new one.
You got rid of the old one because it was not as "stiff", etc, right?
People see such as this and have no knowledge of just what the "substrate" of the part is, what solvents, cleaners, really contain, are they "water borne"(some water borne contain a chemical of the butyl family) which will discolor, in time the part, or "hydrocarbon" based, so are the solvents of a safer, low VOC based or are they of the clorinated variety, such as acetone, MEK (lacquer thinner) or xylene?
Which depending on that solvent system family will/may, create a discoloring of the part forever.
So there it is, just because someone posts on the "internet", does not mean it is an answer for all as an answer to seeking resolution to such a concern.
Grumpy