I would personally like to add a comment about the "Storage Liquid", which you called a primer liquid, on the first-use. (New item.)
That is used machine-oil, and should not be "Puffed". It is high in heavy-metal concentrations. This oil is a sprayed-on or dipped oil, used to limit any corrosion of the heating element in storage. You will find it on most Chinese manufactured metal items.
They dispose of old machine-oil, by filtering it and using it as a general protection oil, to limit rusting or oxidation. (It is cheaper than paying for waste disposal, and cheaper than paying for special made oils for anti-oxidation.)
Personally, I would suggest a single drop of alcohol onto the element wool. Followed by a hot water drip/rinse from the battery-side of the vaporizer assembly. Again, followed by another single drop of alcohol, and another flush with water.
Water will not work, as it is an oil on the device. You need a solvent, and the only safe electronic solvent, which most people have, is alcohol.
I would also like to add... The use of "Club-soda", as opposed to "Coke" or "Pepsi", as the other two drinks contain sugar, which can short-circuit the electrical connections and accelerate the further corrosion, and lead to further wick-gunking. Club soda is pure seltzer water, without sugars. (Carbonic acid) Followed by the water flush, as you mentioned the second time.
Personally, again I would be tempted to use a solvent like alcohol, as opposed to an acid. Since acid will remove the outer layer of metals and any protective electroplating. Baking-soda solution might be a better alternative, but I have not tried that yet. Baking-soda is a buffer, which turns acids into neutral PH-7 and bases into neutral PH-7. (Commonly used where electrical connections and battery acids or other acids exist. It is chemically stable, unlike carbonic acid.)
I wanted to provide some info, for those who may have a concern with poly-fill as the wick, as poly-fill is made from Polyester (Polyethylene terephthalate) or PET.
wikipedia: Polyethylene_terephthalate
PET has a melting point of around 260C or 500F, which is why it may begin to turn brown near the heating element. This is the time when it should be replaced.
PET consists of polymerized units of the monomer ethylene terephthalate, with repeating C10H8O4 units. It contains the chemical elements carbon, hydrogen, and oxygen. If fully burned, it produces only carbon dioxide (CO2) and water (H2O).
plasticsinfo org:/s_plasticsinfo/sec_generic.asp?CID=657&DID=2605
PET itself is biologically inert if ingested, is dermally safe during handling and is not a hazard if inhaled. No evidence of toxicity has been detected in feeding studies using animals. Negative results from Ames tests and studies into unscheduled DNA synthesis indicate that PET is not genotoxic. Similar studies conducted with monomers and typical PET intermediates also indicate that these materials are essentially nontoxic and pose no threats to human health. . . . It is important to stress that the chemistry of compounds that are used to manufacture PET shows no evidence of oestrogenic activity. There is a significant body of evidence that demonstrates that the use of PET is not a concern and is perfectly safe in this respect.
(For those with a fear of the use of plastic-fibers as a wick, as opposed to fiber-glass.)