If disconnecting the tachometer wires while running causes the engine to die, you probably do have a Smiths RVI.
I guess a little more detail is in order. The RVI tachs pass the coil current through an induction loop on the back of the gauge. Each time the coil charges and discharges the coil current flowing through the loop causes a "pulse" and this pulse is used to fire transistors inside the tach circuit. (Not entirely accurate... but that's the Reader's Digest explanation). With the RVI tachs there is no "physical" connection to the coil or its power... just the induction loop.
OEM installs of the RVI tachs involve a white wire from the ignition switch going to the tach, through the loop, then on to the high-side of the coil. On aftermarket installations the common connection scheme is for a white wire to be routed from the coil's low-side (the side going to the distributor) to the tachometer induction loop, then from the loop on to the distributor (points). The result is the same, coil power flows through the induction loop on the back of the tach.
Regardless of where the wires connect to your car's wiring, if you disconnect those white wires, you are interrupting coil power. The engine will die... and with no current flowing the tach won't operate.
For quick contrast, the RVC tachs are a more modern (voltage pulse sensing) design. RVC tachs look for the swing from 12V to 0V as the points open and close. If you pull on the RVC tach wires and accidentally disconnect them... nothing should happen apart from the tachometer not working anymore. However, once the wires are completely disconnected, allowing the sense wire to touch ground will stop the engine as this is equivalent to the points never opening.