The problem is that 1000 grit leaves unsightly marks on the oiled horn, as shown in the picture above.
The majority of answers thus far have been about process and techniques in general or answering a specific question. In light of your last post here, I went back and reread the prior threads and looked at the picture you posted again.
Having done that, I think getting the result you want right now is actually not about going forward to the next steps in progression as if following a recipe but going backward to a step that might need adjustment.
Specifically, I think you began sanding much too soon and the oil was still drying. Penetrating oil finishes can potentially take days to fully cure , and even when fully dry they're still relatively soft finishes. Sanding at less than a day, especially at the horn area where you were not likely to get as significant penetration, was very likely much too soon. Now I can't tell this for sure from a picture but the scratches you are seeing on the horn, I think, are actually in the oil not so much the horn itself. To fix it, you need to level out the scratches, of fill the valleys with another coat of finish, or both depending on their depth (which I also can't tell from the picture).
Wax may well fill the valleys and give you what you want. ...but the negative is, if the wax doesn't give the final result, it's more effort to pull it back and adjust the base finish below it. If it was me, I'd go with the wax on a ho wood handle and not worry much about it. If it didn't cure it, I'd use and enjoy the knife for a while and six months or a year down the road when it's do for a refresher, I'd correct it then. On a fancy heirloom type handle, I'd likely put in more effort to get it right up front. Each there own, though, when it comes to what you want to put the time into.
Here's what I'd do if you want to try and backtrack to fix it (and assuming you don't have a polishing wheel on a bench grinder, or other power buffing/polishing tools):
To level the scratches some, 1000 grit should be more than enough. (Steel wool does work great, but use what you have). Staying in the direction of the grain is fine -give it a gentle wet sanding now that it's sat a few days. Wipe off any residue. Next take an old piece of denim or another rough-ish fabric and buff/rub (any directions you want) ...use a drop or two of mineral oil (butcher block oil) while doing this to lubricate things so you don't accidentally make scratches. See where you are when looking at it dry. May be all you needed, or not. (Added note - If you're feeling very cautious, you can start with the fabric and only hit it with the 1000 if you feel it's not making a difference).
If you still see the marks, meaning they didn't buff out, though they might still disappear with a wax coat, you can get rid of them for certain by adding a final "wash coat" of the tru-oil. take the oil, thin it down a little (maybe add 10% thinner), and wipe on an extremely thin coat with a lint free rag that you balled up. Try and do this in as dust free an environment as you can find. Let that coating sit for several hours...then give it one more hit of the same. It'll dry over night but let it sit and wait at least a few days before hitting it with any sandpaper or abrasives. After that time, you can use denim or canvas as mentioned....or hit it with a light sanding at higher grit if you want ( as general point, I agree with others, sanding above 1000 for a simple wood handle is not really needed....though 2000 may add a hint more sheen. 4K is too much). Finally, put on a wax coating ...let the wax dry and buff it to the finish you want (you can buff it with a dishtowel, wool sock, etc).