Hate to ask the obvious, but did you try replacing the bulb? I can't remember exactly, but that overhead assembly clips into place and can be removed by pulling down on the edges. I remember it being fairly snug..... Also, I don't think there is a relay involved with the function of the dome light.

J. M. van Swaay

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1994 E320 Wagon, 230,000 miles
1995 E320 Sedan, 106,000 miles
1994 E500 Sedan, 79,000 miles