First, many thanks to Art Bernstein, who wrote this on Jan 31:
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"Next time it occurs see if the glow is markedly affected by the turn signal. Then repeat the test with the hazard flasher.

"If so, look for a poor (loose, corroded) connection in the battery junction box in the path toward the ignition switches.

"Probably the best (read easiest) approach is to clean and tighten all that near the battery and the junction box, then see if the trouble returns. Your clue that it stalled was a good one in this case. If still no joy, after tidying up under the hood, consider swapping the ignition switch (electrical portion)."
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OK, so the problem has returned, five months after the battery and alternator failed. The OD and battery light pulsate together, but the headlights don't dim, all the gauges still work, and the car isn't losing power.

The glow is not affected by the turn signal. Occasionally, it is affected by pushing the brake pedal -- the pulses go away for a few minutes. Sometimes it goes away at highway speed, too, without me doing anything.

The pulsating is affected by the forward motion of the car. That is, the speed of the pulses do not speed up then slow down on the shifting of the gears in the automatic transmission.

I have one or two Click and Clack-esque hare-brained theories, such as a worn wire in the instrument cluster that is allowing current meant to turn the speedometer or odometer is getting to the circuit which tells the light to wink on. I also wonder if there is a short somewhere.

Any takers on this one?