:nono: I don't think so...... Lets be real though, 99% of the time you are going to know ahead of time if your battery is starting to die, before it actually does.
I didn't realize that there was 2 compartments in the glovebox door until reading your post. I think you are correct about the oval shaped one on the right side. It looks just about the right size for one of those mini-kleenix packs. I'll have to give that a try.If the glove box door compartment is about 2"x5"x1 1/2" deep, it's for a mini-Kleenex pack. Look in your local big-box car accessory outlet.