I did something similar to mark a table for our club.
Just an assembly table cheaply built from form-ply, but it lives on the club deck unsupervised, and would be easily stolen. So, I marked it to make it less attractive to thieves. The letters are hand painted with a paint brush - if you zoom in you might see that it bled into the grain of the ply, which is fine for our purposes.
The “stain” is vinegar, in which I had left a pound of rusty nails (pallet-pulls) soaking overnight. This photo was taken a few hours after application. The markings have gotten darker with the passage of time.
This technique works extremely well on oak. I’ve seen oak turn midnight-black when treated this way.