Yes, the relays go bad over time. No, there's no other likely cause once you have checked the GPs themselves out.

The 603 NEEDS a good long glow time when cold regardless of the ambient temperature. That extra cylinder makes life hard for the starter! You don't need the dash light to tell you when to start the car... just wait until you hear the relay click off. Either that or shell out the bucks for a new relay. There's really no other solution.

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AlexTheSeal: hack mechanic, inadvertent drifting champ, builder of infernal devices, professional epistemologist

'87 300D Turbo, roadtrip mileage champ (for sale!)
'92 Isuzu Trooper, mudder extraordinaire (for sale!)
'82 Honda Silverwing, cockroach of motorcycles
And various boring daily drivers...