On a Trident you would do well with micro coils. Here's a
video from super_x_drifter on how to set them up. Note the maximum ID for these coils is 1/16". I use cotton in mine and it's great, cheap and easy to do, just don't stuff too much in there or the wick will choke and you'll get burnt hits. Also, leave the wick tails a bit longer than he does because you're not using a Reo bottom feeder like he is.
32 gauge Kanthal is a little thin for this. I suspect it will be a little tricky to keep the coil shape while working with it. I use 28 gauge and that's a lot stiffer. You also will have to keep the number of wraps down a bit to not get too high in resistance. I suggest you try 8 wraps and see how that ohms out.
One more thing. You need to be careful not to go too low in resistance on your mech mod. The lower you go the more power you will draw from the battery. Draw too much and it will start heating up. If this happens it's becoming dangerous. Get it too hot and it will vent and become really bad in short order.
There is a
Ohm's law calculator here. Stick in the battery volts and the coil ohms and hit calculate. It will tell you the amps. You can use 4 volts for the calcs. For battery amp limits check out
post #32 here. Amp limits for some of the more popular batts are listed. If your batt is not listed, Google it. The info is out there. If you can't find it ask here. You need to also be using IMR lithium ion batts.
Vape safe