My 2008 34HT had 4 battys (thruster, house/start 1, house/start 2, plus Gen start) connected to a 3 bank charger by adding a diode isolator. I'm wondering something similar was originally installed on yours and maybe the PO substituted a switch to charge gen start only when chosen manually?
I modified my set up to use the 3 bank charger to charge thruster (now also serves eng start) and house 1&2. Gen has its own Gen and normally takes care of itself when run periodically. I also changed my Gen batty on/off to a off- 1-2-all sw with same foot print & mounting, and use the 2nd position as a jumper to my house batty. That allows periodic charging or emergency Gen start w flip of manual switch.