Follow-up: I got one of the Duplicolor scratch fix pens, in "universal black". So far I have tried it on one of my lesser guitars, as a learning experience, before I try it on the Fender. One of my other guitars, also black, had a bit of a scratch, so I tried out the pen.
Firstly, Duplicolor's instructions suck. Among other things, the pen comes with this weird plastic fork-thing attached to it. It is not mentioned anywhere in the instructions or Duplicolor's Youtube videos, and it makes using the pen pretty much impossible. Apparently it is part of the packaging, and the correct thing to do is to rip it off. Also, you must hold the pen with the abrasive tip up whenever you open it or you risk dumping paint/clearcoat everywhere.
This guy's Amazon review was invaluable and is 1000x better than Duplicolor's own instructions.
The product itself is actually pretty decent, though. The ding I was trying to use it on was really a very superficial scratch, and even a small amount of the paint proved almost too much. So better to use too little paint, since you can always add more! The pen tip also isn't great, since you basically get either no paint or full flow; better to put some paint on a tray and then pick it it up and carefully apply it to the guitar.
But the paint is very opaque, dries quickly, and dries to a nice gloss even without the clearcoat.