Dice towers can be a very effective way of occupying ones hands while focusing on listening, it's not necessarily an indication of inattention.

Reaper is my paint job, but the raptor is the work of my incredibly talented DM! He ran a fantastic campaign, and gave me the opportunity to print and paint a bunch of cool stuff.

What system are you even referencing with this point? I guess sometimes GMs will restrict multiclassing or something, but that's a table issue.