Have the alternator checked. Same happened on my '83 - it turned out to be the first sign that the alternator was going. The voltage regulator in the alternator has three diodes, and one or more can short out, causing the direct path to ground. My battery would go dead within a day or so, just sitting with the key removed. After several (8) alternators in a row that had defective diodes, I got a good one from BMW and it now has about 10k miles on it with no symptoms. Good luck!