I had an idea - Is the radio in your 300E stock or after-market? If aftermarket - how was the anti-theft wiring treated?
Also, if the ignition circuit could cause an alarm and this is one of the more likely palces to get wet - maybe you could check the connections at this point outwards. You may have a trick wire there.
Finally - check the sensors/switches under the hood & in the trunk. Maybe they are gummed up or not functioning properly.
Maybe one of the tech guys will have more light to shed on this.
1988 300E 90k miles "The Cabernet Cruiser"
MBCA - N. Texas Section