Is the spinning wizard AFK, have they disappeared in battle; do they want to give treasure cards to other players, need help fighting a boss or completing a dungeon, can't be disturbed, or are trapped on the Island of GimmieGimmieGimmie?
I'm not the first to suggest having an easier way to tell what another wizard is doing; or wants to do. I believe having floating status badges that either appear over everyone's head, or is visible when you move your mouse over another wizard shall benefit everyone.
Badge colors shall be from light green to extremely dark red; and grow darker over time, or when the task or activity is repeatedly engaged. Multiple badges can also be earned by players as they reach or exceed specific times they've repeated what they're doing.
There could be an input box somewhere to change your status according to whether the player has only menu chat, text chat, or open chat.
If they only have menu chat, there could be a few set buttons to change ingame status, for example: 'Online' 'Busy' (manually set by player) 'Away' (automatically set by system after, say, 10 minutes of inactivity) 'Be back in 5' 'Be back in 10' 'Be back in 15' etc.
If they have text chat or open chat, they could possibly input their own status according to the filters that apply to normal chat.