Given the current ModelView matrix, how can I determine the object-space location of the camera?
The “camera” or viewpoint is at (0., 0., 0.) in eye space. When you turn this into a vector [0 0 0 1] and multiply it by the inverse of the ModelView matrix, the resulting vector is the object-space location of the camera. OpenGL doesn’t let you inquire (through a glGet* routine) the inverse of the ModelView matrix. You’ll need to compute the inverse with your own code.