Lets do this by the book.
1. Get some acetone. Pure acetone. Make a little spot on the finish with a Q tip, in an un noticed place. You can dismount the neck and make a spot on the heel of the neck. If the finish softens after a few minutes, its lacquer, and we'll treat it as lacquer. If not, its some sort of poly, and we'll treat it like poly.
2. If its lacquer... and I'm thinking its not... then you drop fill, or rather, brush fill, many many thin coats, over a period of a long long time, letting each coat dry for a good week or so between it and the next coat.
3. If its poly, then you can drop fill it with superglue, let it dry overnite or even two days.
4. Either way, level sand when fully dry - at least one month after your lacquer, or two days if superglue. Inspect it and see if it needs additional filling to level out. If so, do that and let it dry again......
5. Do your final leveling (and do ALL leveling with a sanding block please!). Then buff out. Both super glue and lacquer will buff out from 600 grit paper, although you can go to 800 on super glue for a bit easier buff. No need on lacquer.
Thats it.
The key - ALWAYS ALWAYS ALWAYS - is adequate dry down. Lacquer is going to be thicker than the original finish - and take next to forever to dry. With lacquer, many thin coats is the key on a fill operation. For super glue , you can get by on fewer, and a bit thicker coats.
Also, for super glue, you might want to try this - mask the area so you get a little bit of ok finish around the bad spot, then swipe on the super glue with your finger. Do that a few times over and over... until you build up finish. When you remove the tape, you'll have a bit larger spot to level down, but it levels so easy, there's no real problem there. It also helps if you lightly sand the area around the repair to get some tooth on it. You can do this once its masked. Something like 320 paper should be fine ... just rough it up a bit.
And thats that