Think of it like this, Formula attaches leads from the battery charger directly to each battery. If shore power is connected and charger is turned ON, the batteries are being charged no matter what position the bat switch is in.

Shore power has to be supplied to the boat, and the breaker for the battery charger has to be on, to pass 120VAC to the bat charger

Thanks for the last two answers!
I'll check this week.

https://cimg9.ibsrv.net/gimg/www.off...bd5e8e7b87.jpg
Okay, it looks like my "charging light" only glows red when the Perko switch is on (1, both, 2)...not in the off position?
It does not seem that this is not too big of an issue for me (compared to the charger being hard wired to the batteries whenever the shore power is plugged in).
Do you think this can cause me issues?
It will take me some time to chase down the wiring.

It could be its fine, but to make sure, its wired the way I think it is, you need a voltmeter.
With shore power and battery switches OFF connect a voltmeter to one of the batteries and record voltage.
Turn shore power ON and leave bat switches OFF and record voltage
Turn battery charger ON and record voltage

With everything disconnected and charged OFF for an hour, you should see close or at 12.7V
With shore power ON and charger ON you should see 13 to 14.5V. Then turn bat switch ON and voltage should not change

Agreed...I have started the troubleshooting.
Thanks!