Here's the way it works. First, imagine the alternator when it's running. An internal current supplied via the voltage regulator supplies the rotor, creating a magnetic field. In order to maintain system voltage, the regulator will modulate the magnetic field and thus the output voltage by varying the current supplied to the rotor.

When you start the car, the alternator isn't initially generating power, so there's no internal current for the rotor. To overcome this, the indicator light circuit is grounded through the rotor. This creates a small magnetic field to get things started. This is what's meant by bootstrapping the alternator. Once the alternator is running and providing it's own power, the indicator light gets 12v directly from the alternator, rather than reaching ground through the rotor. With 12v on both leads, the light goes out.

Since your bulb is out, the likely explanation is that either the bulb or some element of the "D" circuit is failing. (In addition to the bulb, there's wiring, connectors and the ignition switch.)

As to why things look better after you rev. The iron core and shaft of the rotor retain a tiny bit of magnetism after the car is shut down. If the alternator is spun up fast enough, it may be enough of a magnetic field to generate bootstrap current. This is how "one wire" alternators work. (The disadvantages of one-wires are that they need to be goosed to start, and they have no provision for an indicator light.)

The alternative explanation is that there's an internal short in the voltage regulator which is supplying some current to the rotor at all times.

I've installed a small voltmeter in my dash, it's a better way to know what's going on.