Thanks to Hunter D! If you have a P0401 code and determine that the solenoid is bad, needing replacement, absolutely use an OEM part. OEM does not necessarily mean dealership, I was able to find one on ebay for $40ish.

I had previously replaced mine with an auto store part and it cured the code but only temporarily. Yes, on a subsequent test it cycled on application of 12v but according to Hunter D, the solenoid cycles at a high rate and it appears that the generic parts may not be able to keep up the pace.

I replaced mine with OEM and it now cleared the code and some related codes.

Note, the mounting bracket has 3 10mm bolts, two easily accessible from the top and one that is impossible. If you remove the top 2 bolts and carefully bend the bracket back to access the solenoid mounting bolt you can save a headache. Then bend it back and remount the 2 bolts. It's your decision to try this bending method, no guarantee that it won't snap but it worked enough for me to get a ratcheting closed-head wrench on the mounting bolt and made the total job about 15 minutes.

Good luck.

 

UPDATE
I can say that HunterD's advice to use an OEM EGR Solenoid was spot on. 5-600 miles since the swap, clear of all SEL lights and alarms and my fuel mileage has improved 10%.

 

Thanks for the kind words. I will re-iterate - If you need to get going in a hurry (passing an emmissions, etc.) and do not have OEM solenoid, you CAN throw in an aftermarket. However, if you do - order an OEM at the same time (or very soon after) and have it in on hand to be ready to swap when eventually the cheap one will fail.