Hi Dave, assuming you had allowed enough time for the undercoat to fully dry, it sounds as though you didn't rub the undercoat down enough. The best way to do it is to give the undercoat a light coat of a dark colour, you don't have to cover it out, just a light dusting is sufficient. Once it has fully dried, you can them rub it down, this way the dark colour stays in all the low spots & highlights them. You would be surprised just how much is left, it only takes a few microns in depth to mess up the top coat. Make sure you get all of the low spots out. personally I would use 800 grit wet & dry for rubbing down the undercoat, 1200 hasn't much 'cut' & will make hard work of removing the low spots.
If you decide to just lacquer it , use 1200 grit wet & dry, with plenty of water & a little washing up liquid & make sure u clean it off perfectly before lacquering it. Depending on how bad the spots are, lacquer should cover them, you can always rub the lacquer down & polish a finish on it to make it look the dogs things.
Cheers Glenn