There are dozens of variations on this hose theme,but you are pretty right on the money,the EGR is connected to the throttle body "switch" but on some W126's it's also connected to a idle change over switch on the left hand inner fender which in turn activates (at idle) a smog pump with clutch under the alternator.
As you can imagine,all this complexity only works at idle,so lean out the mixture for the test.....