How do you find the ancient mother in endless ocean

it does go to the great drop off. The blue whale and white mother swim besides each other.If you've finished it, you would've seen the cut-scene that showed the Ancient Mother swimming majestically through the channel, and then it would've appeared right in front of you to check out to see the "end" credits.

After that point and for the rest of the game, it swims back and forth right alongside the Drop-Off, just like the blue whale, but a bit further south. It's seriously impossible to miss, and it never moves all year round.
Hope this Helps!