The focus here is making sure that the alternator is charging the battery properly, but the other suggestion I would make is to pull all your fuses one at a time, clean the fuse and holder, and put them back. I like steel wool for jobs like this. I found that my fuses in my '90 and '91 had degraded so much (end connections corroding away) that I replaced all my fuses.

You might pull off the battery clamps and use that steel wool on the clamps and posts as well.

It is a lot easier to diagnose the big problem when all the related systems are clean and working properly. I recently found badly corroded ground connection under the hood of my daughter's old BMW that has been causing an array of quirky electrical problems.