Larry: I have the Beta 38 HP also and do love the engine. I would recommend Nigel Calder Boatowners mechanical and electrical manual (I think the 3rd is the latest edition) as a good place to start researching the issues with multiple battery charging.
I found that on the Beta - you could turn off the key w/o the engine being shut off. Since I wasn't sure how Beta handled the alternator output with the key off and the engine running - I rewired the output of the alternator to always have a load ( battery in this case).
There are also issues with mutliple batteries connected to a common charging point -- if one battery is weak - then the strong batteries will try to charge the weak battery - running all the batteries down etc.
Look into battery isolator ( there are two types - diode and relay) - a way to charge seperate batteries from a single output (your alternator in this case) .
Galvanic isolators are nice addition also.
Also there are multiple types of batteries and each has it's own charging needs/rates etc.
Nigel does a good job with explaining and offers schematics etc. as this is a complicated subject.
Here is a link to a battery watering forum topic.
Hope this helps - and Happy New Year!
Jay