Alternators have diodes that sometimes fail. Diodes in a circuit only allow electrical current
to flow in one direction. Most alternators are not disconnected from the batteries when not running. They have 2 banks of several diodes. If one fails, the alternator
may still function, but will allow current to drain thru the alternator to ground. Without your charger
, the batteries would go dead. It is probably drawing more shore power
Diodes are easy to change. There are sites on the web that sell parts
for most common alternators. I would fix or replace the alternator soon. Many auto parts
stores will test alternators free. Until you fix, you should turn off your battery switch or disconnect the alternator. The current draining is going to ground and might be eating your zincs.