Wait, did i mention somewhere to take the wick out of the coil?
Ah, it must be the "disassemble everything".
I hope you understood by "disassemble everything" unscrewing everything that can be unscrewed? Because i meant unscrewing the drip tip and unscrewing the coil from the base, coil meaning the metal tube containing the actual coil that heats up and the plastic cap that sits on top of the wicks and slides over part of the tube.
There's nothing else can can/should be disassembled. Taking the tank apart is not a good idea. Neither is taking the wick out of the coil, by removing the plastic cap and then pushing the wick up. Because that means you ripped the tank and you broke the connection of the wick with its base.
I did that once just to look inside these things. Nice to see how it works. But by no means i was able to get the two ends of the coil reconnected to the base again.

Luckily i had a spare one.

Ah, you live and learn...