Hi Ralph,
Is there anyone close by that has a negative ground Healey and will be willing to connect and test your tachometer. This would verify whether the tach is performing and the cause is in your electricals. If it turns out to be in your connections, how many loops are in your white ignition wire. Last, and this is a question that just needs mentioning, are you sure the returned tachometer contains the negative ground modifications I assumed you installed before sending?
Although I agree with the Healey Nut's alternate ground suggestion, the ground to the tachometer is shared across all the gauges and, if it were not present, I would expect your panel lights would not work.
Good luck,
Ray (64BJ8P1)