I would use a good quality black fountain pen ink wiped on intitially and allowed to dry off for a few minutes before wiping as much off with a damp (not too wet) rag to soak back up as much of the ink as possible. Maybe hit it again with another damp rag next day and see how things look. Sometimes a very light sanding may be required if too much black is still present. If not enough, repeat same process but don't do a third. Just need to be careful the top doesn't get too wet as that can sometimes caused the veneer and glue holding it onto the body to separate.

Easier than using timbermate as that requires lots of sanding on top of precious little flame veneer thickness.

Never used Limewash but that makes sense if you want a watery milky white appearance.

Cheers, Waz