Unfortunately we are talking about a frequency measuring system here so a voltmeter won't be of much help... you'd need an oscilloscope to see the waveform coming from the W terminal, and a frequency generator to test the tach.
If you have a multimeter with a frequency scale you might be able to detect the signal coming from the W terminal... never done it myself as I have a 'scope. A voltmeter set to the AC setting might actually recognize the signal as well... never done it but it's worth trying now that I think of it.
Grounding the tach input should not have damaged it (although I suppose it might have gotten a voltage spike that did) so I'd be inclined to triple-check the wiring if you're convinced your newer alternator is in fact working... here's where your voltmeter will help you... got a good 12.5V-ish at the alternator with the engine off, that jumps a volt or more with the engine running ?
Failing that, part substitution is another way to go.