Can I charge two batteries through my dual battery system on a single trickle charger, or should I charge each battery separately?
Depends how fast you need them charged. I am assuming you want to connect to one battery, put the switch to "both" and have the charger charge both?
It will work, but the added resistance may slow the charge time of the second battery considerably. Best bet is to do one at a time, or have a charger with multiple bank capability, so you can connect directly to each battery.
Also be careful , if one battery is low and the second battery is fully charged, putting the "switch" to both will cause the two batteries to become equal in charge. The fully charged battery will drain some of its charge to the dead battery causing both to become low on charge. Best to start your boat, then switch to both to let the alternator charge the batteries, or as Kevin said, if you dont have the time, charge one at a time.