Most hand engravers supply places sell a product to darken the background cuts.
They are usually a 2 part easy to use thing. #1 is a somewhat thickened colored liquid that you brush or otherwise cover the engraving with and let dry.
The second part is a solvent, usually tri-chlor or similar, that you carefully swipe over the dried part#1 surface on a swab or cloth patch leaving the color in the depths of the cuts.
N-Graver sells one (I see it's OOS now though)
Scroll down page for the listing. Go to their Price List for that.
http://www.ngraver.com/finishing.htmRioGrande.com sells their own brand and sells it separately parts #1 and #2.,,and in Brown, Gold, ect.
https://www.riogrande.com/product/midas-background-antique-and-solvent-kit/335400You can probably find others, they are all about the same thing.
They hold up pretty well in service. Solvents that approach the level of the Part#2 of the product will of course break them down and remove, but you don't hardly see that used on your fav SxS much in everyday wipedown.
Ultra sonic cleaners will remove them after a few go'rounds but they stay put pretty well for a while from that,, very nicely from everyday wear & use. That from jewelry experience.