It does, this is very similar to the one that I own. They came in many variations (3 different levels of reeds, with/without cassotto, with/without MIDI). Mine was the top of the line model with hand made reeds and Cassotto. Mine also has the optional MIDI out installed on the tone generator.
To answer the question, yes the jack is a stereo jack with the controls for the left and right hands individually controlled. The original cable is a "Y" cable... one stereo jack that splits in to 2 mono inputs. Though I still have the original one, it developed a broken wire at the "Y" connection and I replaced it with a new one decades ago.
As far as the tone generator not sounding good, there has to be something wrong. The electric sounds of the Elka may be dated but they are high quality... not even the Roland 8X has as high a quality trumpet sound as this accordion has. I've spent many an hour enjoying this accordion.
@jdam01 : Please feel free to document your process, I may wish to duplicate the process. I also have the schematics for my accordion, including the tone generator. Let me know if I can be of any assistance.