What a coincidence....our '03 started doing the same thing a couple of weeks ago as well. I'll add the dashboard lights dim when these warning lights go on. For everyone playing along at home, the dash looks like this when it happens:
(EDIT: Sorry, for some reason I can't add pictures today)
What's frustrating (yet intriguing) about this symptom is there is no error code.
I have not yet solved it. I'm going to replace battery cables and then move on to the alternator. There was an old service bulletin at one time that made reference to 'fan circuit noise' and suggested alternator replacement (I'll attach this service bulletin pdf is someone can let me know how or turn on access):
Export Service Bulletin
2003 American Honda Motor Co., Inc. – All Rights Reserved XTB 25098 (0304) 1 of 1
April 2003
03-902
Applies To: 2002 Odyssey – ALL
Charging System, Door, and Brake Light Indicators Come on While Driving
SYMPTOM The charging system, door monitors, and brake light indicators simultaneously turn on and off while driving.
PROBABLE CAUSE Electrical noise coming from the cooling fan circuit causes the indicators to flicker momentarily. NOTE: This electrical noise does not affect the alternator’s output, nor apply to any other alternator problem.
CORRECTIVE ACTION Replace the alternator.
PARTS INFORMATION Alternator: P/N 31100-PGK-A03
WARRANTY CLAIM INFORMATION In warranty: The normal warranty applies. Operation Number: 118100 Flat Rate Time: 1.0 hour Failed Part: P/N 31100-PGK-A02 Defect Code: 067 Contention Code: B02
REPAIR PROCEDURE Replace the alternator (see the 1999–03 Odyssey Shop Manual).
When mine happened the first time, I was driving during the evening with headlights. If the charging system hadn't been working correctly that night I certainly would have run out of battery charge in a few miles and would have been stranded (I made it home and there doesn't seem to be a charging problem). So the mention above re the charging not being affected holds true according to my experience so far.
I running on an aftermarket alternator that is only 2 years old but I can't remember which brand (I think it was a white-label from AutoZone). If I do move on to replacing it, I'll go back to Denso or shop for the replacement P/N mentioned in this service bulletin.
I'll keep updating this thread.