The place to test to see if the egr holds vacuum is point 6 in the diagram above. No experience w/Ford EGR systems – at least the modern version – but I believe the EVR is the gadget on top in your photo link, and point 6 is where the rubber vacuum hose connects to the metal nipple. The computer programs the EVR to output a certain % of the manifold vacuum to the EGR’s diaphragm input (metal nipple).
So to test if the EGR diaphragm holds vacuum you’d remove the rubber hose and connect your vacuum pump to point 6. this test is done w/the engine off. I expect your vacuum pump is faulty if it only pumps to 10, but usually if the egr diaphragm holds to 10 inches then it will hold to 20, so I doubt that’s the issue.
The test you did where you connect a vacuum gauge to point 6 with the rubber hose disconnected and your read 20 inches with the engine running, not sure what that means. I wouldn’t expect you’d get any reading at all unless the diaphragm wasn’t intact. However if you connected it first, then started the engine you might could get a vacuum reading there b/c the engine vacuum might pull downward on the diaphragm and result in a vacuum above the diaphragm. Most vacuum pumps have a release valve so you could release any vacuum from that effect, then close the valve and if you still were getting 20 inches, that could indicated the egr diaphragm is incontinent. The diaphragm is that thin horizontal black line above the pintle in the diagram above.
If the EGR is working and you connect a vacuum pump to point 6 and pull 20 inches of vacuum at idle, it should stall or nearly stall the engine. A vacuum above the diaphragm creates a force that pulls the pintle upward, opens the valve at point 3, and allows more exhaust gas to flow into the intake manifold.
The testing you did is a good start, but isn’t quite the tests needed. The silver nipple register 20 inches of vacuum makes me suspicious however that your EGR’s diaphragm is faulty. Suggest to return that new vacuum pump you bought and ask for one that actually works. I have one made by mity vac (as I recall), have had it for 20+ years, and it works great. Harbor Freight has a considerably less expensive version of the same idea, but no experience with that one. It’s a good idea to purchase a separate vacuum gauge too. It’s possible to measure vacuum with the pump alone, but if you want to continue diy’er diagnosis you’ll run into limitations without having a separate vacuum gauge. A vacuum gauge is quite inexpensive.