PLEASE HELP with difficult to diagnose electrical problem
 

HELP PLEASE. This car is my son's first car, and I was hoping to have help with this problem. Our 1996 Eclipse's 'dummy' battery light has been coming on randomly in the past 2+ months. My mechanic has given up trying to diagnose actual problem - he installed a new alternator (twice) that didn't fix the problem. He hooked up a alt meter so we could see what happens with the charge before the 'dummy' light comes on--he suspected it might be overcharging, not undercharging--but it is hard to tell just what is going on. Before the dummy light comes on, the alt meter needle is all over the place--spastically flopping from under to over charge--within 5 min after this occurs, the dummy light come on. There are two other scenarios with the meter --it eaither runs right on 14 volts without wavering or it 'vibrates' -- like a bumpy road might affect it (even when not on a bumpy road) I believe when it is running on 14 without 'vibrating' it is running properly, but when it 'vibrates' it is not running properly, but not bad enough to trigger the dummy light. One clue to ponder: when the light comes on, turning off the car and restarting it, makes the dummy light shut off. There is no pattern if it will come on again or not. This perplexing electrical problem baffled my mechanic, and he now thinks it is probably a faulty computer system ($400) and I should take it to a dealer to diagnose. Any experience with this problem before? We cannot afford a new computer system.