The EGR itself can get carbon in it and keep it open, as well as the electrical part failing to close it.
Definitely sounds like a vacuum leak (egr valve opened at idle would be one too). Check the T under the snout, it's bad for doing it. Don't forget the elbow on the throttle bodies and map sensor (this is kinda hidden).
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'13 Mustang 3.7V6 - MT82
'00 GP SE (L67 Swap, XP, Headers, 3.25")
'98 GTP, '01 Bonne