There’s a fundamental limitation in containing enough solids to provide opacity, while still having a medium that can flow through a paint nib/tip, which is essentially a filter. The finer the tip, the less opaque the medium will be.
Maybe a syringe with a fine needle tip and water based acrylic paint would yield better results? Or the bottles/tips used for dispensing acrylic weld solvent.
I’ve used toothpicks dipped in airbrush paint to fill tight engravings and it seemed that the acrylic engraving literally pulled the paint droplet off the toothpick and flowed it level.