I've spoken to every person I can and I searched just about everywhere.
The Giga Drain TM is on a tiny clearing of land off a river on Route 209. You can get to this route by going east out of Hearthome City.
This text tutorial has step-by-step screenshots that guide you the whole way. The TM's exact location is shown in the image below (taken from the same tutorial link).
It's near one of the rocks.
This video from Youtube tells you exactly where to find it.