It never hurts to stack several patches( charred clothe) together, around a piece that has an ember burning on it. You then can blow the ember to ignite the other pieces of charred clothe, too. Combined, wrapped around the wick, you can get enough heat to melt the wax to its gaseous state, and ignite the fumes that come off it.
Most people think what burns in a candle is that wick, because they see the tip of the wick glowing. What you are really igniting- and why it takes a bit of time even holding a flame from that lighter to the wick to get a flame going-- is the gas coming out of the wick from the melted wax. The wick serves as a vehicle, to draw the fumes from the melted wax up and feed the flame. If that cotton wick is Not surrounded by wax, it burns so fast it makes your head spin.
So, heat up the wax with your charred cloth, and don't ***** foot about doing it!
Its frankly much easier to blow an ember in charred cloth into tinder and start a separate fire there, followed by using that flame to ignite a candle, than to try to ignite that thin wick on a candle from even several layers of charred cloth feeding an ember(s). But, it can be done.