The problem I see is that both batteries are treated as primaries in our dual battery system (unless yours didn't come with duals from the factory). As John said, they want consistent draw, and for that matter they should be identical in age and type, and should be replaced at the same time. If I was going to isolate two, I would swap the system to one (huge) battery for starting, and then rewire for an auxiliary battery for your accessories.

Instead, I've chosen another route. I have left the factory system as is, and isolated a third battery (in the back) for accessories, such as inverters, camplights, etc. I also have a momentary switch so I can parallel the three if I've run the two mains down (two yellow top hybrids, so unlikely).

Used this setup: http://www.ase-supply.com/Sure_Power_1314_Battery_Separator_p/sp-1314.htm