Does anyone know a way to “color” height maps to generate a semi-realistic 3D rendering?
Depends on what look you want to achieve, a realistic one that is often referenced is “Ambient Aperture Lighting” . Another one I found interesting and more “cartographic” is .
Edit: there are plenty of citations of  which implement extensions to it like global illumination, etc.
If I understood the question correctly, then my advice would be first try the classic way of coloring valleys green, highlands brown and mountaintops white. Basically map height of each point to a color gradient of your choice. See this picture for an example.