Since the fretboard is a polymer, AKA plastic, you will not want to use any oil based products on it as they will deteriorate the material. Waxes while safer are also not recommended as they will not bond with the surface and gunk up as it collects dusk and grime.
For the best results, you will need a buffing machine for some sort. You can use a power drill attachment or an actual buffing wheel. Hand polishing is not possible as it does have enough force and speed to resurface the fretboard effectively. Do not use a Dremel as it spins way too fast and will cut into the fretboard. Use painter's tape to cover where the body connects to the neck to keep the compound and buffing wheel from damaging the body's finish. Remove the tape and wipe away the excess polish with a lint free towel when done.
Product: Formax - PLASTIC-GLO (Ultra Fine, Dry Grade) 515-6163 P-22
P-22 Plastic-Glo is an ultra-fine cutting and high coloring compound for bringing out a smooth, brilliant finish on practically every type of plastic. No. P-22 is a pure white compound on the very dry side. Will not glaze on the buff or load up compound into crevices or recesses of the work. Being exceptionally fine, it will not scratch the softest plastic. Nothing better for producing the very finest finishes on transparent plastics.