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
Here's where my ignorance may really start to surface. You're talking about the voltage regulator, correct? the regulator mounted on the firewall? That's what I disconnected, and when disconnected, the tach did not work at all.

When I was probing the alternator, I had my meter set to AC, and wasn't sure which of the probes should go to the output stud, so I tried both. (one at a time, of course...haha) Here's where I think I screwed up: with one probe touching the output, I touched the other to another terminal on the alternator. I don't remember which gave me the high voltage reading and which gave me the low, I'll redo the test tomorrow when I'm off work. Are you saying I should ground the meter to an engine ground and not one of the other alternator terminals?

The tach is not connected to coil neg, as I'm concerned with voiding the warranty since I have an ignition box. But I am 100% certain that the wire going to coil negative is coming from the ignition control module. The wire going to coil positive is brown and coming from the ballast resistor.

@Bewy not a and idea, I'm just not eager to disconnect it yet another time....

Apologies for my ignorance and I appreciate everyone's help here.