Might be awhile, but I will post pics when done.
It seems that the air comes from the holes of the cylinder, and not from below. A vertical coil may be inapplicable or useless here. And I still can’t understand at all where is the tank where the liquid is poured.
P.S.:
...I understand, this is "drip", not tank. And it is possible to use vertical coil here, but it will be a strange coil

1. Unscrew and return into the box 2 of the 4 bolts (this means 2 of the 3 lower bolts). They will not be needed.
2. Don something round on the center pin. For example, a mouthpiece (if possible).
3. Fasten 1 end of the long wire at the bottom with a bolt using any of the 3 holes at the bottom.
4. Wrap the wire around what is don on the center pin to have a wide spiral. The number of turns is best determined empirically, it will depend on the thickness and material of the wire.
5. While holding the spiral in place, remove from the pin what was worn on it.
6. Bend the wire so that it makes contact with the center pin, cut, insert and fasten in the hole.
7. Burn the spiral if necessary and if possible (depending on the material).
8. Now cram more cotton
into (not outside!) this vertical coil. And fill this cotton with liquid.
0. The principle: more coil diameter - more wire - more evaporating surface and more resistance - less wattage, less temperature, more vapour.