E46 Intermittent Battery Light

I've got a 1999 323i, and lately the battery charging light on the
dash comes on and off intermittently. It seems as though it comes on
when I'm moving over 25 mph and goes off when I'm idling at a light or
something. Then, the other day the car randomly stalled out twice
while sitting at a light. It started right up again though!

This sounds as though the alternator is on its way out, but I want to
try and narrow it down before I go ordering a new one. Any
suggestions, things to check/try, etc?
I'd appreciate any help.
Thanks,
--Ryan