I'm adding color to a black and white engraving. I understand about creating a new layer for the color. But how do I make the original black and white image appear "on top" of the color layer?

You can set the Engraving layer blending mode to Multiply and then put your paint layers below that.

I’m not sure that this solves my problem. I want the black lines of the engraving to be on top, and the color layer to be behind it, so that the black lines of the engraving are sharper. I tried what you suggested, and I can’t get it to work this way. In fact, the color from the brush seems to only apply to the edges of the black lines of the engraving, which is not what your screen shot shows. 

The new layer will be transparent; so it can stay on top. Change the blend mode from normal to color. When you use the brush tool to paint, the original engraving should show through - click image