I have experienced voltage regulators that require a battery to function to full voltage. Most gy6 Chinese scoot reg/rect are like that. No battery and you get 6-7vdc, and you fry the regulator eventually. With batt, 14vdc and everything works great.
You don't need much of a battery for them to work if that's the case here.
Small drill battery? That's what I use on projects that req batteries.
Dewalts work really well, got a bunch at a garage sale awhile back. (edited)