I'm familiar with this set up on some English built boats.
If you have a flat starting battery the principal of the rocker switch is to group all available amps to start the motor, as soon as the motor fires evenly release the switch and the system will revert to normal charging, be aware however that the starting battery was initially too flat to start the engine so give the boat a good run to recharge the batteries.
With a twin engine boat, normally when one engine is running it should charge both starting batteries and after 15 mins or so be able to start the second engine.
PROVIDING the previous owner hasn't 'modified' the original installation.
Before you use the boat again, check all battery connections are cleaned absolutely pristine and coat the connections lightly with Vaseline(petroleum jelly).
Check the electrolyte levels in all the batteries, if necessary top up with distilled water. Use a good LED torch, DO NOT USE A NAKED LIGHT WHEN CHECKING THE BATTERIES ACID LEVELS.
Add it to your list of pre start list of checks.