There's actually two power inputs: one from the battery that is alway on regardless of key position, and a second from the switch that is on only in the run position. If you have a bad connection between the battery and the GP relay, or if your GP relay internal fuse is dodgy you might confuse this with a relay problem. Better to check the connections and operating voltages (voltages at the GPs when relay is energized, switched voltage to relay, ground connections, engine ground, etc.) first before replacing parts. Also, take the fuse out of the relay and make sure it is in one piece. Sometimes they develop a hairline crack that interferes with proper operation.

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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)