Long story short: I am sharing a blend setup that will mimic the engraved line cross-hatching style that one sees on old, old documents (see US paper currency for examples, or some of the clip art that Terry Gilliam used in Monty Python television shows, for examples). I think of it as just ‘engraved’ but others tell me that this look should be called “copperplate engraving.”
This Blender file uses compositing to filter your rendered image(s). There are controls (labeled) in the Compositing nodes view.
This file comes with a set of images, to be used as engraving lines. I guess you could substitute any images you wanted, but make sure that you adjust the “Line Weights Master” node so that your engraved-line source images are large enough to cover your render. I.e., if you’re rendering at 3840 pixels wide, you’d need to double the scale because my images are only 1920 px wide.
I got a lot of help from blender artists here over the years and this is my humble attempt to offer something helpful in return.