Well, any tach needs the negative coil hookup to determine rpm. So that's my guess as to where to connect the single wire. Negative side of coil has +12v, just with rapid cycling between +12v and zero volts when running. Your tach probably has a capacitor inside to provide a steady voltage for the operating electronics. Grounds through the case/mount. That's my best guess how it works and connections.
The single wire tach , was normally used with Diesel engines , it was triggered off stator windings on the alternator
Which tach? https://www.westach.com/tachometers They tell you what signal it takes....when you click on the link for that tach.