I do not know if I can help or not. I have a 1991 350SD, and have yet to experience the problem you describe, but seem to have had just about every other problem the car can conjure.
I also have owned a number of older Diesels, and none of them have an electric fuel pump. I do not believe the newer ones have them either. So the trickle of fuel you describe is likely normal, unless it is less than a steady stream.
On my 350SD the factory installed alarm system is controlled by the driver door lock. I have had the local dealer estimate the cost to repair the unit on my car as the alarm sounds periodically without reason. I was told the faulty part is in the driver door. Trying to start the car will not clear the alarm, you have to lock and unlock the driver door to clear the alarm, so I do not think the ignition switch has a control function, although I imagine it can cause the alarm to sound if it is activated out of sequence. Good Luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)