Installed new coil, now the tach acts funny

OK there is no way that the tach should quit when you disconnect the regulator. Something is amiss there

The reading at the alternator is troubling. Can you detail how you came up with 33v?

You might try that again. You do know what I mean, right, the output stud of the alternator is the large black wire and this is hot at all times. This is what goes in, through the ammeter, and back out to the battery

With the car running on fast idle, hook one lead of the meter to ground, and the meter set on AC volts. Now hook the remaining meter probe to the stud. Again, you should get a very small voltage reading, the less the better.

"While you are there" also take that same reading with the meter in DC volts. Note the reading and take it again with headlights turned on.

Is the tach now reconnected to coil NEG? And have you made certain that is the wire going to the ECU? (Not the power wire) If there is any question of that, one way to find out is to pull the connector off the ECU box, disconnect the coil NEG wire and measure power at the coil + You should see battery voltage. If not the wires are reversed at the coil