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Hi there,
OK, I believe it is entirely normal, and here is my idiotic explanation:
The battery light is wired between the alternator D+ (field source) and ignition-switched battery.
In lamp test mode, key on, motor not turning, it lights because the field winding, through the regulator, provides a path to ground in the quiet alternator.
When you start the motor, the small amount of current passed through that battery light bulb generates enough magnetism in the field winding to act against the rotor windings, allowing the alternator to begin to produce charging voltage. This is analogous to a bootstrap.
Once the motor is running, the rotor windings generate the supply for the field winding to the D+ terminal, through the small field diode array.
When you shut off the motor, the ignition-switched side of the lamp then becomes a path to ground (through all the loads switched by that circuit, such as the ignition coil) and for the time the alternator still spins, the field excitation voltage is still available at the D+ (terminal 61) connected to the battery light.

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Art Benstein near Baltimore
Drive carefully. It's not only cars that can be recalled by their maker.
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