My father is experiencing double vision (quality: with both eyes open) change in his left pupil direction. possibility of 3rd nerve damage?

Get seen now: This needs to be investigated by a competent physician. This can be anything from an infarct of the third nerve from vascular disease to new-onset multiple sclerosis. Don't try to diagnose it yourself. I'm glad you care about Dad. Best wishes.

See specialist: Double vision of sudden onset needs a work up,to determine the cause. Then, you can make a correct diagnosis, and treatment plan