Is ambient lighting related to GL_LIGHT0? In other words, do I need any lights at all enabled (apart from enabling lighting itself) to use just ambient lighting?
Each light have it’s own ambient light, and you must have that light enabled for the ambient light to have any effect. However, there is a global ambient light, which is not tied to a specific light, and to get that you only have to enable lighting, not a specific light.
Check out glLightModel and GL_LIGHT_MODEL_AMBIENT. Default global ambient light is (0.2, 0.2, 0.2, 1.0).