Voltage steady when drawing on battery, but jumpy when on Alt..why?

I am still in voltage jumpy hell. Now wife is making fun of the pulsing lights on our 66 dart with the HEI and elctronic voltage reg. I won't list the numerous things I have tried, so this question is more of an "enlighten" me moment.

Why is it that if I load up the electrical system enough so that the battery kicks in, at that point the voltage is dead stable, with no pulsation at all, solid. But as soon as load is lightened and the battery no longer needs to help, then my voltage gets jumpy and lights begin to pulse.