Yes, just go up through the grades, although there is probably a very real risk of rubbing through. It all depends on how thick the original clear is and how much you've taken off with 120.
Theres no real method of which grades you should use. The more grades you can use, the less work you need to do with each grade. Ideally you want to remove all the scratches made by the previous, coarser grade, so if you jump too far between grades then you'll just have to work harder. Maybe move to 240 now, then 320, 500, 800, 1000. As you get to the higher grades you won't have to rub much at all.
You will probably be able to polish it from 1000 but if you have it I'd go to 1500 and 2000 just to make life easier.
Maybe when you see the black begin to thin move to the next grade to give yourself a better chance of not breaking through.
It looks like it's had a neck pickup at some point in it's life.