COLREGS Rule 30 indicates that a boat at anchor in a specialized area under 20m does need the anchor light illuminated. Given that the whole purpose of the COLREGS are to "avoid collisions" I routinely have mine on at a mooring.

Last October at the Great Harbour PI around 200 am 2 power boats of islanders started fighting on the Willie T, hopped in their boats and then chased each other through the mooring field in their boats for about 10 minutes. I turned on every light we had until hey headed to Tortolla.

I very much apologize to the star gazers among us.