Another piece of the puzzle required to understand whether the pen 'obviously' falls or not is, 'what kind of atmosphere does the moon have'?

Another unobvious fact is that the force that holds up a floating object is also tied to weight - specifically, the weight of the atmosphere or liquid. Even if the atmosphere on the Moon were precisely as dense as the Earth's (it is not), the pen and the air would be lighter in the same proportion, and the pen would still fall.

Edit: i.e. what bentarm said.