I called support and we are doing a cross-ship RMA.

Thank you for your reply.  That was my question in my first post above:  Is this normal behavior?  If a couple of people had responded to the affirmative, then I would have connected it to my system.  But in absence of that, I don't want to put my system at risk for damage.  Nobody answered my post in a morning's time and with Christmas coming up this week, I decided to call support for the same advice.  To their credit, they responded faster than this forum, which is almost unheard of for an 800 number these days!  I'm not blaming anybody here of course; it's possible that nobody here knew the answer to my question and so didn't respond.  I wasn't expecting nor needing a dozen "I don't know" responses. 
 
Anyway, I described everything as in my first post above, and the EVGA support rep suggested that we do an RMA. 
 
To be clear, I was only asking for his advice and he knew that.  I did not demand an RMA but he suggested that we just do one, and he offered to help me with it even though this was an Amazon purchase.  Besides, it's being cross-shipped, so I will have both on hand at the same time.  If the new one passes the tester, then I'll know I did the right thing.  On the other hand, if the new one fails the tester like the old one did, then I'll call support again and we'll figure out what to do.  Maybe this IS normal behavior after all, but right now nobody seems to know.
 
As for the test-block...the fan SHOULD spin up when "eco" mode is disabled.  As described in the manual, my post above, and relayed to the support guy.  He seemed knowledgeable about the product and did not oppose me or try to tell me that there's "no way" the fan wouldn't spin up with the test block in place.  Now maybe you're right on this too.  If so, we'll find out soon enough.
 
Thanks again! 
 
P.S.  Diagnostic tools are often used to "pre-test" a device before installing it into a system.  This tool is much like a (very) specialized multimeter, and I know a lot of people who'll test a new PSU on a multimeter before installing it.  We know what the specs should read for the 24 pin, PCIe VGA, SATA, and peripherals.  It seems perfectly reasonable to test it first before installing it into a $2500 system that is old enough now to make motherboard, memory, CPU, and GPU parts replacement difficult and/or expensive.

Not many users would test a new unit. Glad you have it sorted, nice PSU. I hope to upgrade to that unit for the efficiency.

Thanks guys!  I'm not an engineer but I live and work among several, so maybe some things have rubbed off on me; zebras' stripes and all...   
 
Part testing can't easily or feasibly be done for EVERYTHING you install into a computer, such as GPUs.  But a PSU can be tested quite easily and it's basically connected to EVERYTHING.  A dodgy PSU has the means, opportunity, and maybe even motive to leave a swath of destruction, so I like to test these whenever possible.
 
Happy New Year!

Cool GTX
May want to edit your Title to say ------ Solved

Done; thank you for the reminder!

Hello; it's no problem adding to this thread if you think your problem is the same as mine was.  But if your problem drags on for a bit you may want to open your own thread because mine says "solved" in the subject line, so some folks may no longer be watching. 
 
I have a 1200 watt P2.  It would stand to reason that your G2's Eco mode should work the same way as my P2 (G2 probably part of the nomenclature for "Gold" efficiency and P2 is probably intended to mean "Platinum" efficiency). 
 
If you are using an electronic tester that puts a load on the PSU, then yes the fan should spin while Eco mode is "disabled", and the fan should not spin when Eco mode is engaged (but once you fire up something heavy like a game, Folding at Home, or some sort of CPU or GPU compute activity, Eco mode should let the PSU fan turn on automatically). 
 
That I can confirm.
 
But once I figured out that the cause of my problem was a bad cable that came with the first PSU, I did not think to retest either the first PSU or the RMA cross-shipped second PSU with the little "dummy plug" that comes in the package.  I think it "should" work the same way, but I don't know for sure because I have not confirmed it, and the good motherboard cable is now installed into and snaked around the box, making testing impossible without several hours of work and rework, for which I don't have the time.
 
These PSUs have a long warranty period; just make sure you register it.  If you suspect yours is bad, call EVGA.  They did a good job with the cross-ship for me, and the only complaint I would have is 7 days it took to arrive but then it WAS the week between Christmas and New Year's, so I can't really complain.
 
The first PSU is all packed up and ready to go back to EVGA.  I put a big tag on on the bad cable, so hopefully it won't end up going to somebody else.  I'll be making a UPS run shortly.