Does this sound like an ALTERNATOR...?

OK... My cousin has an older Ice Cream Truck that has had all kinds of
problems lately.  He just had the engined serviced.  Last week his fan
belt broke.

Now...  here is what is happening.  He will be driving slowly through
the neighborhoods for a few hours and after while... whenever he hits
the brake his music box will seemingly go real low and at a slower
rythem.

Next thing you know, the engine will run very poorly and it will
stall....  He needs a jumpstart to get going again.  In the
morning...  he needed a jumpstart once again.

He took it to his mechanic who said that the problem was caused by a
low idle... which was speeded up somewhat.

The first half of today...  everything went smoothly... but about
6:00... it died again in exactly the same manner.

Does this sound like an ALTERNATOR?  Are alternator and charging
issues hard to diagnose?  Could a very weak battery ever cause any of
the above symptoms?

It is very frustrating.  Any educated guesses?

Thanks in advance.

annie