After many hours of reading forums, watching youtubes and googling the P0410 code, I found one very straightforward, and easy troubleshooting procedure on the internet. I know that it is completely appropriate for at least both W210 and W211 (it is listed as a W211 article), if not many other chassis models. It covers the air pump, solenoid, and check valves. The troubleshooting procedure is the technical article found at Pelicanparts.com here:
Secondary Air System Troubleshooting Procedure

If for some reason the link doesn't work, you can just google this technical article and it will probably the the first on the resulting list when you use these keywords:
secondary air pump pelican parts mercedes

The fuse and relay are not covered, but they are easy to check just by starting the car in the morning, when the engine is at room temp [mandatory], and determining if the pump is working or not for about 30 seconds. You'll hear the vacuum cleaner noise at the front of the engine for ~30 sec or so until it shuts off. (It may help to first disconnect the thick rubber tube at it's central connection to the air pump as in Figure 7 of the Pelicanparts procedure.) If not working, then check the 40A fuse and the relay, usually located in the box on the passenger side of the engine compartment. It's a standard 4-prong relay, so check Youtube for how to check relays with a voltmeter.

One extra step: If after doing this troubleshooting procedure you find that everything is working, then the problem is almost certainly a clogged passage in the head that goes from the check valve to the exhaust manifold. You can determine whether it is the left or right side by taking off the check valves, starting the car (cold or warm doesn't matter), and you should be able to feel and hear exhaust pulses coming out of the head's exposed passageways where the check valves attach. If it is weak or nonexistent, then the passageway is blocked in the head on that side. Try some carb cleaner, poking with a wire, air pressure, etc to try to clean the passageway. I've read that one should be careful about putting WD40 or other oily sprays into these passageways, as they may damage the catalytic converter.

At anytime, you can manually turn on the air pump for various tests by just using jumper cables or other wires to run from the "+" 12 volt battery connection under the hood (and a negative connection to any body bolt) to the pos and neg connections on the secondary air pump after removing the electrical connector from it. Note that the air pump's pos and neg connections are marked (as I remember, the "+" is toward the rear of the car, but check this), which may be important if you want air to be pumped versus sucked.

Some other tips:
- You don't need a vacuum gauge to determine if vacuum is present. Just put your bare finger over the end of the tube and your finger should stick to it if there is vacuum.
- To manually apply a vacuum, you can either use a hand vacuum pump like those that come with brake bleeding kits or use a hand-pumped oil changer (like the Mityvac 7400 fluid evacuator). The check valve opened on my car after about 5 pumps of my Mityvac oil changer.

Hope this helps. Good luck.

 

Great! Sounds like you're offering to freely share your DAS! Please leave your phone number so all those in your area reading this who don't have a DAS (most of the viewers) can contact you!
What a guy!
By the way, for 90% of the causes of the P0410 code, it would only take minutes, not take many weekends, to fix the problem. Exceedingly simple, especially after one has the info I supplied above. I'm surprised you don't know that.

 

Plutoe, I think its great that you and a minority of others have expensive DAS analysis systems to diagnose cars (really, I'm happy for you), but most readers of these forums don't have them or know anyone that does. Those are the people I wrote my post for and not for DAS owners or professional mechanics. I think it's not really very collegial of you to criticize my post for trying to help those people. Yes, I do believe that the vast majority of cases that have a single P0410 code will have a problem somewhere in the secondary air pump pathway (for example, fuse, relay, secondary air pump, solenoid, electrical connections to those items, check valves, associated vacuum hoses, or clogged head passageway), so I think my post is valid in the majority of cases of a single P0410 code and will help a lot of people and save them from having to gather that info piecemeal like I had to do. Like you, I am a believer that some single codes can be caused by a lot of seemingly irrelevant problems, but it's safe to say the majority of single P0410 codes will have a problem in this pathway (could always be a small minority of exceptions, but not likely).
I wish you all the best, as I am sure you probably have helped people in other threads -- you're just not helping much in this one. You're of course free to reply if you wish, but I will not be responding further to you in this thread.