I remember being told during my own flying training (albeit on a Cessna 150) that if the 'Low Voltage' warning light remained lit, then the engine should immediately be shut down.
Surely you mean the starter solenoid energised light which should extinguish after you release the starter key and if not a shutdown should be made immediately.
The low voltage light is something else but they are not the same thing.
So long as people are trained and qualified and properly supervised doing a running change in a PA38 should not present any undue hazard.