Check for a short in the door. The alarm lead is a single wire that comes off the lock mechanism. I had the same problem on my 300e. It was in the passenger door. The lead was grounding to the door sheetmetal. Taped it up, problem solved. Good luck, hope it's a simple troubleshoot and fix.

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Jeff L
1987 300e
1989 300e
1987 BMW 325