For just 1/16 there's several things to try.
Oldest trick in the book is to mix sawdust of the same wood with PVA (Elmers, Titebond, etc.) glue to make a paste.
Elmers makes a 'dark' glue you could mix with the sawdust to possibly better effect.
Mahogany has a pink cast and so does Bondo so that's a good filler. The wormholes often found in mahogany are filled with Bondo as recommended by Jeff Jewitt in his book Hand Applied Finishes.
If the miter is tight on the inside and gapped on the outside you could simply roundover the corners with router bit or sandpaper.
Finally, you could force the sawdust into the gaps and then shoot with the lacquer to set it. Then lightly sand as you would to level the lacquer between coats, anyway.
Let us know if any of these methods work.