A minimum of two weeks, but I'd wait a month if I could as it should then be really hard.
To get a good gloss finish, the surface needs to be flat (not just feeling smooth), with no small dimples in the surface. I'd start off with P600 and work up to P2000 before switching to 4000 Micromesh. 4000 Micromesh has 5 micron particles, P2000 has 10 micron. The smaller the steps between grits, the better the end result as each smaller grit should remove the scratches made by the previous grit. To big a jump and the bigger scratches are still left. Ideal you'd go to 3600 Micromesh after P2000.
It really is good to get a full range of wet and dry papers P240-P2500, and the Micromesh range from 1500 up to 12000.
The micromesh grit numbers don't correspond to the P grit range, so you need to look at a conversion chart such as this one to see how they compare e.g. Micromesh 1500 fits in between P600 and P800 whereas the number alone makes you think it's a lot finer.
https://www.thesandpaperman.com.au/a...ion-chart.html
Some people stop around P2000 before switching to polishing, but I prefer to go finer, and for a small area like a headstock, it doesn't take much effort to do so.
Once the surface has been levelled, you don't need to push hard at all, just run the paper/micromesh over the surface lightly and let the grits do the work. Pushing hard is likely to leave small scratches that will take the edge off the shine.