I'm looking for help finding the cause(s) of the battery draining on our 1983 300CD-T (Calif.) and would appreciate any ideas or suggestions.

This problem has been present for probably five years (or perhaps longer) - I'm getting old and memory ain't what it used to be!
Current mileage on the vehicle is about 247,000.

Symptoms:
Every three to four months, I'll get in the car and try to start it and upon turning the key to the pre-glow position, the instrument cluster lamps are all off and of course, the starter won't turn (like this morning). I can usually jump start the car.

Background:
1. Every other week, I drive the car to and from work, Monday through Friday (roundtrip is about 26 mi.). On the "off" week, the wife drives it around town on two or three days.

2. Battery replacements:
2001: 228,600 mi.
2002: 231,800 mi.
2004: 240,800 mi.
2006: 242,400 mi.
2008: 244,900 mi.

3. When I start the car (when the battery has sufficient charge), it starts and idles just fine. HOWEVER, while idling, the battery light in the instrument cluster glows bright red. If I never press the accelerator pedal and just sit there and idle, the light remains on no matter what. This seems like a clue that something is wrong. All I have to do is to rev the engine once, the light goes out, and never comes back on.

4. The last time the alternator was replaced was in 2001 at 229,800 mi. At that time, it was replaced with a Bosch rebuild. About six months ago, I had the alternator tested at a local auto parts store and it tested as ok.

5. I disconnected the antenna a year or so ago and that did not appear to affect the problem.

6. I have confirmed that the trunk lamp is not on when the trunk is closed.

7. I have confirmed that the courtesy lamps (front and rear) are not on when the doors are shut and the devices are turned off.

8. I have confirmed that the ground strap near the transmission is securely fastened.

9. I have confirmed that the ground wire by the antenna in the trunk is securely fastened.

10. Headlights, taillights, turn signals, wipers, horn, fuel gauge, power windows, emergency flashers, radio, power outside rearview mirror, glove box light, fog lights, climate control/fan, instrument cluster lamps, tachometer, and defroster: none appears to be on when it shouldn't be and all appear to work properly.

11. The cruise control doesn't work (I don't think, it has been a while) and neither does the power sunroof.

12. Clock in instrument cluster keeps accurate time.

13. The vehicle is stored in my garage in Phoenix, Arizona.

Any ideas for methods to track down the problem(s)? Special tool(s) to use?

Thanks-