I have got a 95 E320 Wagon, and here's the scenario with the factory alarm.

No Keyless Entry System

I can lock and unlock the driver's door and the alarm doesn't come on, ever. However, if the alarm is already on, I can disarm it from the driver's door. On the passenger door, I can lock the car and the alarm doesn't arm, but if I unlock the car from the passenger side the alarm comes on! When I lock the tailgate, the alarm arms, and when I unlock the tailgate, it disarms. The tailgate seems to work fine. No idea of the cause, and it is annoying since to have the alarm on you must lock at the tailgate.

Does anyone know about this?

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1995 MB E320 Wagon, 41k
1992 Land Rover Range Rover, 186k
1996 Volvo 960 Wagon, 105k
1996 Ford "Exploder" Limited 2wd
1982 Volvo 240 GL Diesel, 157k (61k on new gas engine conv.)