The Curt Echo Trailer Brake Controller # C51180 needs to have a 7-way blade connector on both the tow vehicle as well as the trailer.
The Custer Trailer Connector Adapter # ADP7R-7B that you found is designed to adapt a vehicle with a 7-way round pin connector to allow a trailer with a 7-way blade connection to be towed. It will not work properly with your trailer having a 7-way round pin male connector.
The Pollak Trailer Connector Adapter # PK12728 will convert the 7-way round pin... view full answer...