Re: Does this sound like an ALTERNATOR...?

Test with a volt meter across the battery.
You should have about 13.2 volts with the key off. If you don't, try
charging the battery over night with the battery cables disconnected.
If it still isn't up to 13.2 volts then the battery is shot.
Some batteries don't stand up under load. You could also do a load
test.
You should have about 15 volts across the battery with the engine
running. If it isn't somewhere close to that voltage then likely
either the alternator or the voltage regulator is bad.
A lot of auto parts stores will do battery and alternator tests for
free. You just have to take it in and they test it. Call around.
I think an ice cream truck would put a lot of stress on the battery
and alternator. If you need to replace the alternator then ask for the
biggest one you can get, maybe a 105 amp. If the battery is shot then
get the most powerful that will fit in your battery box.