My parents' Peugeot 505 diesel had that issue from time to time before we sold it, and I never figured out the cause. You would just have to turn the key on & off and back on until the GP light lit, otherwise, the GP's wouldn't go on at all (and engine would crank endlessly and not start). I think it was the relay starting to fail, but it could have also been the ignition switch wearing out and not activating the GP position. Or (less likely) possibly an intermittent connection somewhere in the wiring.

These would be some things to check...I doubt it's an individual plug in this case. We got lucky that the only time we couldn't get the GP light to go on at all after multiple tries was in the garage at home, and it worked fine again the next day.

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1976 240D "Katja"