alternator or battery?

[David M. Hoffman]

'95 G20

The battery and brake dash (idiot) lights come on simultaneously when
the car is idling.  It is an intermittant problem, but it has happened
with greater frequency this past week.  The belts are good and have the
proper tension.  At idle with the accessories off, the voltage across
the battery terminals reads 13.8 V.  With the engine off, the reading is
around 13 V.  I have not measured the voltage when the dash lights are
on because they go off after only a few seconds.

The archives suggest an alternator or battery problem.  Is there a way
to tell the difference?