Fiddling

Interesting expression I've never heard, but seems to apply quite often.

fiddle while Rome burns

Occupy oneself with unimportant matters and neglect important ones during a crisis. For example, The account was falling through, but he was more worried about missing his golf gametalk about fiddling while Rome burns! This expression alludes to the legend that the Emperor Nero played his fiddle while watching the conflagration of Rome. [Mid-1600s]