with my drivers door, I ended up needing to replace the key/seat belt buzzer relay behind the instument cluster. same symptoms no dome light with driver door open, it would work with pass not driver.
The indicator light is below the center counsul under the carpet there is a screw that needs to be removed. remove trim from gearshift then carefully and gently pull on back of counsul to lift rear and pivot forward

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1988 300TE
1979 240D
1979 300SD(R.I.P. Hit by somone running a red light)