88 Honda Accord battery light go on then goes off

Normal 0 When my battery light came on I first thought it was my alternator (it was replaced over a year ago). Then I tried cleaning my rather corroded battery terminals and the light when off, problem solved. Two days later it was back on so I cleaned the battery terminals again, they had a darkish gray film on them, but no luck, light on. Maybe I need a new battery? At this point I thought alt. problem again. For some reason (other than running a bit rough) I revved it up over 3000 and light when off until it dropped below 3K and it came back on. I did this for a few mins and finally the light went off. A couple of days later with the light on I went and had my battery checked. It tested OK. They said the terminals were corroded and cleaned them. The light was now off again. Every time the battery light goes off it stays off until the next day or a long time between driving. Looking at the battery (over 5 y/o) it seemed to have a wetness around the positive post so I thought maybe the battery could be leaking and causing the corrosion. The next day of course the light was on so I naturally cleaned the terminals again and the light went off then I went and replaced the battery. The next day the light was back on. It seems that the light will go off when the car warms up but not all the time sometime all I did was clean the terminals. Could this be a wiring harness problem or is it going to be a 300.00 alternator replacement? I have other mechanical problems I would rather spend the money on since it has 148K on it and who know how long its going last. If it weren’t so hard to get to I would do it myself. I will test the voltage on the battery with the light on and when it goes off to see if it matches what I've heard they should be.

Thanks for any information