yeah, you can burnish the wood with a micro abrasive sandpaper but it will be a pain to do well without removing the frets. Start with a 15 micron paper (1000x) and next with 5 micron, (2500x) finishing with .5 micron (9000x). Keep in mind that rosewood is a ring porous wood so it won't look as shiny and smooth as ebony, which has no visible pore structure.
Alternatively, you can apply a couple coats of tung oil, letting each cure first, then buff to a low luster sheen. It won't be glossy, but it will provide some luster. It'll take a couple weeks to do properly by letting the oil cure.
Btw, make sure you use real, 100% tung oil. Many products that are labeled as tung oil are not -- they're a wiping varnish. Formsby's, minwax, etc are examples of faux tung oil. Check the label, if it lists petroleum products as part of the composition then it's not tung oil.