What is the ruling on dyeing part of the beard black to fill in gaps, without the presence of white hair?

It is permissible to apply black color to the skin to fill hairless gaps, as long as it does not contain impure ingredients or form an insulating layer that prevents water from reaching the skin during ritual purification (tahara). The prohibition of dyeing with black was specifically mentioned for hair, and the default ruling for such ordinary matters is permissibility unless there is evidence to the contrary.