The EGR valve can leak in 3 ways.
Suck on the small tube with a bit of hose and the diaphragm should hold the vacuum. Leaking will not effect running. At idle there should be no vacuum on the line from the solenoid.
The exhaust path can leak and let exhaust into the intake at idle and make for rough idle but should not mess with fuel trims.
Air can leak in through those vent holes through the shaft seal and let air into the intake. That would lead to higher fuel trims at idle.
So a exhaust leak through will make for bad idle, slow idle. A leak of air though the haft will make for high fuel trims at idle and may make high idle.
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Suck on the small tube with a bit of hose and the diaphragm should hold the vacuum. Leaking will not effect running. At idle there should be no vacuum on the line from the solenoid.
The exhaust path can leak and let exhaust into the intake at idle and make for rough idle but should not mess with fuel trims.
Air can leak in through those vent holes through the shaft seal and let air into the intake. That would lead to higher fuel trims at idle.
So a exhaust leak through will make for bad idle, slow idle. A leak of air though the haft will make for high fuel trims at idle and may make high idle.
-chart-