Justin, thats an awesome sled!!! I am glad you found this thread of interest. While I am no pro, I spent many hours tinkering on these girls.
Start from the tank first and work your way up the fuel line. If original, there is a fuel T under the cowl below the starter, right hand side. It has a check valve in it and is a pain to remove, I have yet to do mine. My other Ghost has some plaque in it and my primer jammed up.
A standard cheapo snowmobile primer fits like a glove and works just fine. There is a spring loaded needle valve on the intake runner so if you pull it apart, be careful as its easily lost. A chunk of bic click pen spring works in its absence.
If the impulse line from the intake, through the various gaskets to the pump is sealed correctly, make sure the pump is clean. There is a mesh screen inside that catches debris. If your sled runs good on restart, the pump is probably fine but maybe an air leak somewhere that has to purge.
Now the hardest part of carb is removing it. Be very careful on the throttle cable. It uses a little cotter pin, which is a pain to remove and install and easy to drop. Use a 90 degree pick to straighten it and pull it out.
9/16" socket and extension to remove the carb. There are locks on the nuts but you need to do some creative hand posturing so you do not loose the locks, nuts and gasket.
If cleaning, strip it down and spray out the low speed circuit on the top. The high speed is simple. Just clean the carb body, brass emulsion tube (9/16" head) and use a fresh o ring. I cannot recall the size right now and will look tomorrow. Use a bit of silicone grease or Vaseline to reinstall and I think its 3/16" float height. Thats all she takes. You can make a bowl gasket from cereal box if needed. Older Harley 's used a version of this carb if you need a rebuild outside of what I mentioned. The o ring fixed the erratic high idle at operating temp on my Evinrude, the flooding on my first Ghost and the rich bog on this new one.
Factory hi lo settings are 1.5 turns out each. No less that 1.25. Mine run better around the 2 mark.
I use a resisted spark plug, just have to check this week what I used. Works fine but allows me to use my multimeter to test voltage.
Clean your battery ground and the CDI grounds. They caused spark issues for me. If in a pinch, disconnect the ignition switch (Indak is the OEM and still in business) and kill switch (big cause of spark loss). It will pull start, run with no lights and choke to kill it.
Thats a start but these are heavy sleds, not fast but comfortable and higher features.