Not having any expertise in electronics, assumed that an electronic tacho as used on our machines would be a counter of the pulse produced for each revolution of the rotating member, whether on a lathe or a mill.
If that is the case, the magnet passes the Hall sensor and produces a pulse (Sine wave form? ) one per rev, which the board counts against a time base and displays the count per minute.
Presumably the original sensor still has the pin out intact, so a replacement, wired in the same configuration, should function in the same way.
If the machine is belt driven, there will be a chart showing the speed for a given pulley /belt layout for a single phase motor running on 50 Hz or 60 Hz supply.motor.
If the machine is VFD driven, and if you want to be confident of your speed read out, a separate tachometer is needed as a datum.
Howard.