I made the black tattoos on the model on the left by sliding vertices and coloring the faces. Of course this messed up the topology of the face (which I would like to animate). I've been trying to use texture painting to achieve the same look of the model on the left on the model on the right without sliding the vertices and messing up my topology. I can't figure out how to do this. I've come close, but I'm sure there is some concept concerning texture painting that I don't understand that keeps me from getting the result I want. How do I make these black tattoos without messing up the topology using nodes in cycles?
If you want to do this with Blender texture painting, use the stencil brush mode:
Stencil will allow you to "spray through" a 2D image to project it's patterns onto the mesh.
To back up to a more general sense, the way I'd approach this is to build the tattoos marks on a 2D sheet using your drawing/image editing tool of choice (Illustrator, GIMP, Photoshop, whatever). Then you can either use a projection tool (like Blender's stencil paint or the projection brush in Substance Painter) to spray the appropriate symbols into place. Symmetry can help you keep them even on each side. Alternately, you can lay the symbols into place in a 2D editor, but this requires a UV sheet free of distortion and with seams out of the way (such as the back of the head).
Doing this via a texture will also allow you to use a lower resolution face mesh, as you might find the one in your file tricky to weight paint and set up shape keys for.
I finally figured it out with the help of someone at Blender Discord. I used texture painting and the node setup below. The key is the RGB to BW node. This allowed me to paint two separate materials onto one quad face. I appreciate your help, @JtheNinja.