Hardly the former. It's 12 hours no matter what the pencil is doing. Idle or working. I'm on my second pencil since I thought my first one was bad. But I am experiencing the same thing. Since the pencil has no off switch, the battery drains regardless if it is being used or sitting on your desk.
Charge the battery to 100 percent and by night, with no use, I'm down to 10 percent. Other folks say their experience is different. It's possible that I have a second bad one, and maybe there are bad batches?
Seems to me Apple could have built in an off switch. Otherwise the alternative is to turn off BT and then reconnect the pencil after turning BT back on.