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My 98 does something similar. I am at low speed, below 25. I have watched the voltmeter and it drops about the same time when the AIR pump kicks in, lights dim etc. Are you seeing a voltage drop when the dimming occurs and is it all speeds/rpm?
First check all your connections and see if they are good. Second check your battery to make sure it is good. If you have a non-gel battery check for any leaks underneath the battery on top of the computer (bad).
My problem eventually came down to replacing the altenator and then I never had the problem again.
I do admit it was very annoying once I started to notice it..