[Healeys] Electrical Question

[PG]

The car starts on jumpers from another vehicle..but, as soon as the jumpers
are taken away, the car dies...  

 

Even if the battery is bad, should the car not run on the generator?  Unless
of course, it is bad.   It reads about 12 volts but vascilates sometimes
down to 4 or 5 volts then back up again...rapidly.   The Battery is old and
is likely finished.  However, should the car not run regardless?  

 

Paul