Use and trust the TTL meter of your camera. Use the fastest shutter speed possible to minimise camera shake and subject movement, also use the smallest aperture possible to ensure good depth in field, so that the entire animal is in focus. Whenever there are only a few frames left in the camera, it is better to rewind and load a fresh roll, so that at the next clicking opportunity, you have an entire roll to shoot and thereby not miss a chance because of time lost in reloading the camera at a crucial time. Always keep exposed film separately and safely. Avoid the mistake of reloading exposed film once again into the camera by always rewinding exposed film completely into the cassette without leaving the tongue of the film out of the cassette.
Most wild animals are less shy of a riding elephant.
It can take one quite close to animals even in impenetrable tracts, but the chief drawbacks are the steep angle of view one gets and the element of camera shake due to the movements of the elephant. Shooting more frames to increase the chances of getting a few sharp pictures, shooting from a distance to reduce the angle of view or waiting for the animal to move to a better location are tactics that may be employed to work around this. Follow the rhythm of of the elephant and click when the animal is steady, and in a phase of least movement. Unfortunately, the best action of the subject, and the moment of least movement of the elephant may not always coincide. Never get down from a vehicle to approach an animal on foot in the hope of getting closer to it.