The light bulb in the dash is the only bulb involved. It is flickering so it is not burned out. That bulb serves as resistance to drop the voltage a tad to avoid burning up the alternator . Some GM cars had a resistor paralleled across the bulb in case the bulb burned out. I've not seen one on a Regal but there might be some.
The question is this: Is the alternator bad, or does the bulb in the dash have a flaky connection to the pc mylar. If you want to find out, rig a jumper with a small bulb in the middle to act as resistance. Hook one end to the battery or back of the alternator post and the other end into the brown wire coming from the dash. When you turn the key on, this bulb should light up and burn steadily. When you start the car up, the light should go out and the alternator should be charging.
If the alternator is not charging, then you have a bum alternator.
