You're both right :) An anchor light is supposed to be 360 degrees, your son
is right about that.
However, boats under a certain length (forget what it is, but its longer
than any potter) don't need to show an anchor light unless anchored in a
fairway. State rules may vary, but most of 'em follow USCG rules.
At anchor I usually turn on that light for visibility (some is better than
none) and figure if the CG bothers to hassle me on their way back from a
drug bust that I'll claim i don't need a light at all...
The stupid little light they put on the front of our masts of your boat and
mine (#461) is really all wrong. It IS a 360 degree light, but they mounted
it in the vertical plane, so half of that 360 is UP. I'm sure the thought
process that went into this and a lot of other hardware on potters of our
vintage was "hey, its a CHEAP light, close enough".
A proper anchor light, of course, would shine 360 in the horizontal plane.
So, you can consider it a steaming light - but a proper steaming light would
be 225 degrees.
On my project list is to put a proper combination light (225 forward, 135
rear) and wire it such that it will work for sailing (running lights only,
mast lights off) steaming (forward light and running lights only) or
anchoring (forward and rear lights, no running lights).
Chapmans (you DO have this don't you?) explains it pretty well, so does the
Annapolis book and most others.