I neglected to say that we finally bought the car battery jumper that BK has. With three cars here, and given BK's experience with AAA, it made total sense and I'm glad we have it. However, either the voltage meter or something else is faulty, or I'm understanding something wrong.
When pressing the red button before charging it the first time, it read somewhere in the middle which I'd expect with it being new. Then I gave it an initial overnight charge. When I unplugged and checked it the next day, the needle only went into the low green so I plugged it back in for a few hours. Unplugging and checking it again, the needle now doesn't even move. But when it's plugged in, the "Charged" light is on.
So, question for BK: I'll read through the instructions again but it seems very straightforward. I'll also contact the company. But does it sound like I'm doing something wrong?
EDIT: I just checked it again after leaving it alone for a while and it jumped right up to 13 volts!