Find the light circuit breaker of the elevator. Its Always separated from the controls usually on the emergency panel (generator). Have a outlet installed on that circuit at the breaker panel. Find yourself a internet over power adapter Net Gear or an even better an industrial version.
Most elevator cars I have worked with already have an outlet near the controls on the top of the car tied into the light circuit.
If this isn't expensive enough for your client there are several companies offering a complete solution in a box.
you can use any onvif camera with this solution.