But not when the key is removed from the ignition, unless....

I think you may have mis-wired your ignition switch or it is probably more likely that you have a shorted wire somewhere. The two circuits share the same wire that goes to the hot side of Fuse 12 from contact 15 (Circuit 15) on the ignition switch . Check that circuit with the ignition OFF. (Do your windows work with the ignition off?) It should not have any voltage. If that line has been connected to the battery or some other 'always hot' circuit, then it might display the symptoms you note. Your glow plug relay would always have a "RUN" signal, and may only reset and actually start glowing when cranking. It would also begin a glow cycle when you attach ground. Try attaching the ground with the ignition in the RUN position, and see if the glow light comes on.

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mjk

'84 300SD 119KMi (Liesl der Diesel)
'84 300D 326KMi when the oil left (former parts car)
'82 300SD 253KMi (new parts car)