Your converter, in its original 1983 form, was only there to replace the battery if you had shore power available. That's what the switch is for, it selects shore power or battery as the 12v power source. It is also not designed to recharge your battery from shore power.
I would replace it with a converter from Progressive Dynamics, I bought a new PD9245C from Amazon for around $150. With it you can run off shore power and charge your battery (intelligently, 3 stage charging) at the same time. The downside is it is not by any means a unit that will fit in the stock location. I believe WFCO has one to fit the opening for the old BW's