2 Centurys, same electrical problem

I have an '86 Century with a 4 cylinder engine. I had at one time an '85 with the same engine. The '85 developed an electrical power drain problem. I gave the car away. Now the '86 has developed the same problem...that is the battery drains while the car is parked and inactive. I have a new battery, had the alternator checked, the battery itself checked, and all that.

Does anyone know of any Buick recalls or bulletins or have any kind of info on this problem. I don't find it a coincidence this has happened twice with two different cars.