when the car is running the coil wire should be in A/C voltage, not D/C. I think you have the wrong coil wire going in to the tach. Thats the input to tell it how fast the engine is spinning. It creates an A/C voltage that goes up with RPM.
You want to ground the black lead and use the red lead to test whichever wire you think is your tach signal wire coming off the coil. Like I said before its A/C so make sure you set the DMM to A/C voltage. The right wire will go up in voltage with RPM's. It was dk. green/yellow on the stock coil, but I remember you saying you had an aftermarket.