keeping those batteries separate while gaining the ability to motor charge both is a little more complicated.
Nah..............
http://promariner.com/products/prolsocharge-series/
I have ran one of these (three batt's) for maybe two yrs now, not an issue yet. Works quite well and doesn't need to parallel the batteries to charge a battery.....i.e., once started, it senses when the start battery is full (1 minute or 20 minutes) then switches it out (if V alt < V Batt, see below) of the charge circuit and routes all the current available to the low/exhausted aux battery.
Some other iso systems will/can only parallel the exhausted/low aux battery with the now full start battery, wasting energy sometimes by back charging one battery into the other if the alt supply voltage drops below the start battery voltage. This drop in alt voltage occurs when say a 10A (20A, 30A, 40A, 50A....100A) system (Your Shindengen reg/rec looks like a 10A unit) is trying to charge a battery that is drawing higher then 10 Amps.
This/these types of iso prevents this by switching into anti back charging mode and are optimized for that if and when a battery requires more charge current that a alt can provide. Even my 40A wimpy merc system, sometimes it isolates two of my three batteries when the third battery is pretty low due to it being used to make coffee with a 750 Watt inverter.
Once the aux battery is up to snuff, the system will then parallel both the start and aux batteries, keeping them both topped off. It'll jump back into the anti back charging mode though anytime you pull down one of the batteries too low.
If the motor is running and with your 10,000 lumen light, you should draw about roughly 11 Amps, with both batteries topped off, it will iso the aux battery pretty quick once your switch it on.
Of course when the motor is off, all batteries are auto-magically isolated by default
It works for me and how I use my systems, seems your need might be similar ......GL