Leave it on both or open and hook yr charger up to 1 battery. If yr charger has the capacity this will do the job. If yr charger isn't big it should still be ok it will just take longer.

Leaving your batteries on a trickle charge will see them die an early death, if you do it you will need to top up the water on a pretty regular basis (if they are not sealed.) Also a good idea to keep the motor isolated from the charging current as some motors electrionics get fried as a result of the charging current going through the motor. Rather expensive lesson to learn that one!

If your batteries are in good condition and getting charged off the motor there should be no real need to have them on trickle, they should be able to last 3 months without a charge, if not there is an issue such as battery is on its way out or something is draining your batteries.

 A good charger like a Ctek will not do damage to a battery as trhey have a mode that vertually put no amperage into the battery when they reach the final of the 7 charging stages. Having said that and as said above, if you use the boat regularly, the batteries are in good condition and the charging system on your motor is normal, there is no great need for trickle charging.

The problem is extended no use periods longer than a couple of months, especially if the is any leakage or needed current flow. Cars and bikes with immobilisers are especially good at destroying batteries if left unused.

I amd getting much longer out of the batteries on my Dirt and road bike now that I am running a Ctek charger on them.

The bottom line is, batteries last heaps longer if kept in a fully charged state.

 As i said above mate if you want to charge both batteries have isolator set to open or both , if charging 1 switch to that battery and hook yr charger to it. You don't have to disconnect anything just hook charger to battery. CTEC chargers r our best seller in the shop cause they r simple and reliable to use. They won't damage yr batteries they r designed to maintain them cheers.

 as sulo said  keeping batterys on a constant charge will see them die earlier , lead acid batterys are ment to be discharged and charged to keep them in good health 

 It's not a constant charge , all batteries discharge as a matter of course the c tec smart charger goes into maintenance mode and keeps them topped up. The deeper you discharge a lead acid battery the harder it is to get it back to full or 12 - 13 vlts.