So here’s an error that, at the time I encountered it, did not have a great deal of information about it on the web:
The system definition with the same name as this data source already exists in the Business Data Connectivity Metadata Store and it refers to a different data source. Cannot complete operation generation. Add a connection to this data source with a different name and try again.
I encountered this error after deleting an External Content Type, then recreating it with the same name. The solution ended up being rather simple: close SP 2010 Designer and reopen again. Voila!