welli tried and failed,
just could not get the coils close enough (must be my sausage fingers,
hay ho back to buying coils.
Not that I have attempted a coil rebuild yet but wire I do know a fair bit about. (and I haver sausage fingers too.)
For the actual coiling the whole thing about using a needle/cocktail stick is the best thing it serves as a "mandrel" for the coil.
Personally I wouldn't cut the wire from the main reel before hand, that way you can't end up with it too short or too long and then end up wasting wire.
The best way I have found to coil wire is to always have a slightly longer tail wire than needed (only a couple of mm) hold it in place on your mandrel/cocktail stick/whatever with the thumb of your left hand (if you are right handed.)
Then using your right thumb and forefinger slowly coax the wire around the mandrel (given that we also have the wick to contend with you may find it easier to use low tack masking tape so the wick doesn't move around and stays tight so you don't end up trapping it.)
If you are aiming for 6 coils stop at 5.
then use the tail end to make the 6th rotation, holding the wick at the other end of the coil and push the coil together as you make the last rotation.
Then you can fold up the tails and finally cut the wire off the reel.
I hope that makes some sort of sense as I am trying to translate from wire wrapping world to vaping world but it may help someone.