Someone mentioned there is 1000+ techniques to apply CA. Here's mine.
HDPE bushings (non stick to CA).
Grit 180 radial (lathe on), lengtwise (lathe off). Inspection of high/ low spots. More sanding if needed. quick wipe with paper tower (dry) to remove extra dust and grit leftovers.
Grit 400 radial (lathe on), lengthwise (lathe off). Inspection again. paper towel again.
Grit 600 radial and lengthwise sanding. wipe with DNA and peper towel (again, radial with lathe on and lengthwise with lathe off) then with the dry paper tower I clear the wood again.
For applying CA i use plastic bags on my finger (comes with pen kits) and strip of paper towel. I do 3 coats of thin with 2 drops of CA on paper towel (if i need to grain fill the wood i pour about 4-5 drops directly on wood and spread it) let it dry ~30 sec. then do another light pass ( I think light passes is a key to great shine).
If i'm happy with the result of thin CA I move on to medium and do another 6 coats.
After that i let it dry for about 10 minutes and then move on to sanding the CA. I start with 600 grit (light passes), wipe of the dust, then 1000 grit, and sometimes if i don't have nothing to do more i do 2500grit. again sanding radial and lengthwise
Fully wipe everything off and turn to the micromesh wet sanding. (always use clean water and clear pads) This time i sand only radial with lathe on (500 rpm). move on to 12k grit and don't wipe it with paper, let it dry by itself.
No polishing needed, deep, exposed, smooth gloss is guaranteed.
Good luck. Btw everything i learned about prepairing and sanding and coating is from this forum, so don't be lazy and search

Cheers.
PS. cut paper towel between aplications of CA. don't tear it, because it will leaves tearouts of paper which can get stuck to your job. use scissors for nice cut.