I don't believe the 380 had an EGR until after 1984. My 1984 380SE (CAL Emissions Version) didn't have one, nor was one called out on the sticker. it did have the air pump that yours has. Your sticker doesn't show or list an EGR valve.

Change the air pump filter in the Air cleaner, put in a new Air filter, change the oil, oil filter, to fresh and fill up with Union 76 91 Octane gas(10% Ethanol). Go drive the bejeebers(30 miles or 30 minutes) out of the car to get the cat hot, then go to the Smog test shop with it hot. Hope you have changed out the Dist cap, rotor, Wires and spark plugs too. This all helps. Also you can remove the air filter from the Air cleaner,(before the 30 minute drive), to do the test and that also will help.

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1986 Euro 500SEC "RUF" 9:1CR, "Rose"
1985 Euro 500SEC Cabriolet AMG Widebody
1982 Euro 500SEL "Blue"
2001 Texas Heeler (Aussie/Queensland X) "Sulphie",
2012 Queensland Red Heeler "Squeak"
Best dogs I've ever had.