I spent a day struggling with this recently. I watched every video on You-Tube, and I still couldn't get it to work. I finally found a thread on arfcom, and combined that info with a crafting blog I found...
1)Use a Q-tip or small brush to cover the engraved area with paint ( I used Testor's due to availability and selection of colors, gloss & flat, although I suspect nail polish would work fine)
2)take a piece of cardboard or heavy cardstock or plastic and scrape off the excess
3)Let it dry for 5-10 minutes and wipe off what little is left on the surface. Here is the trick I found on the crafting blog.....use a page of telephone book paper folded over to make a stiff, flat pad. Dampen it with mineral spirits and rub over the area. The flat, hard surface will not lift the paint out of the engraving, but will take it off the flat surface.
Using this method, I got GREAT results even on shallow engraving, and it only took one coat to fill the engraving. Every time I tried using paper towels or rags, the soft material would scoop the paint out of the engraving, but the paper was too stiff and flat to do that. Worked great for me.