I had a thought that perhaps you have a relay that is stuck. I did some searching and found this:
GROUP 63 Lights Bulletin Number 63 03 87 (1548) Page 1 of 2 Montvale, NJ January 1988 Technical Dept. SUBJECT: Headlights/Foglights MODELS: E30 - Model Year 1988 (produced prior to 10/87) Complaint: One or all of these symptoms may occur: 1) The headlights may remain "on" when the ignition is turned OFF. 2) Battery discharged (dead) due to relays remaining energized. 3) The fuel gauge needle indicates between 1/8 to 1/4 with ignition and headlights turned OFF. Cause: Improper relays installed (without diodes). Note: The purpose of the diode is to prevent the unintended energizing of the relay.
Repair
Procedure: Only perform repair procedure if the power distribution box is a Version 2 (8 relays). Verify that part number on relay matches the number listed below:
Note: These numbers can be found on either the top or side of the relay.
Parts
Information: If an improper relay is found, replace it with one of the following:
Description Part Number
K3 High Beam 61 31 1 386 557 K4 Low Beam 61 31 1 386 558 K8 Fog Lights 61 31 1 380 013