I'm not familiar with the cutout you have.
You now say that yours is a 12 volt system. ("I do not think that I informed you correctly, in that this is now a 12V system from original..if that makes you change your advice.") I don't think your 3 brush generator is compatible with a 12 volt system/battery....
8040-6159 *NEW* Universal Generator Cut Out 6V, 12V, 24V | Smith Co Electric
Brand New High Quality Universal Solid State Replacement Generator Cut Out - No Adjustments
This is the more common type of cutout