Above are photos of the old and new tach faces. (The old tach does not work. The new tach's pointer points to "zero" when 12 volts are applied to it.)
Below are photos of their backs.

     

As seen other places on this website, I have checked out both the "power" and the "pulse" circuits available to the tach, have video-recorded the tests and have displayed the videos on youtube. They are available here:

Here are the wiring instructions for the new tach:

Today I am wondering why the new tach needs 12 v. power fed to it, while the old tach did not.

Any ideas? (facebook exchange follows)

Fred Costa - what is the little digital looking display at the bottom of the guage? This could be the 12volt requirment.

Frank Miklos - I would say that it is the digital display but the new one we got for the 58 Coronado has both also and no digital display. It may be that the old one is analog and the new one is digital (meaning the internal workings are digital). 12v may be necessary to run a digitally operated tach.

Grant MacLaren - I like both reasonable responses. I had completely forgotten about the engine-hour meter low in the new tach's face. Thanks!