As mentioned the tach is taking a reading off the flywheel at the back of the engine. I would look at the connections there, making sure they are clean, and at the back of the tach, making sure they are clean and tight. The actual pickup rarely fail as it has no moving parts and are taking a magnetic reading as the teeth on the flywheel passes by. The only time I've heard of one failing is when it vibrated itself out too far to sense the teeth going by.
When you find the sensor make sure you are getting power at one side of it. You might look here and see if this helps even though it might not be exactly what you have, the concept will be similar. They also have a decent schematic. Good luck.
Troubleshooting Teleflex Tachometer Gauges
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Tachometer (Magnetic Pickup) (Code B)
(For Diesel or Gas Engines with a Sender Mounting Point in Bell Housing or Adjacent to a Rotating Gear
This tachometer is for a diesel or gasoline engine having a sender mounting point (3/4-16 thread) in the bell housing (or adjacent to some other rotating gear), and 12-16 VDC (24 Volt systems can be accommodated with a Voltage Reducer).
Check all wire connections to see that they're tight and not corroded. NOTE: Some older style tachometers operate with only Ground and Sender connections. Teleflex tachs must have 12 VDC (from the ignition switch, "ON" when engine is running) to the "IGN" stud.
When tachometer is first turned on, pointer must go to zero 50 RPM. If not, check connections (if OK, tachometer is probably faulty).
Voltages with engine running should be: IGN to GND terminal: 12-16 VDC. SEND to GND terminal: 0.3 VAC minimum at idle; (voltage will increase with engine speed).
Set rotary switch on tachometer back to the range that includes the number of gear teeth that pass by the Magnetic Pickup in one crank shaft revolution. This information can be obtained from the Engine Distributor or Dealer. Arrow on slot must point to setting; if it is between settings, the tach will go full scale when engine is started.
Final calibration requires a Remote Master Tachometer. Connect Master Tach and start engine. At about 1,500-2,000 RPM, use a jeweller's screwdriver to carefully adjust the potentiometer in the "CAL" hole (about 10 o'clock on the rear of the tach), bringing the tachometer into agreement with the Master Tach. Only a minimal turning is required. Overtorquing of adjustment will damage gauge mechanism. Turning clockwise increases tach reading, counter clock wise reduces reading. If the tachometer cannot be brought into calibration, the black Range Selector Switch is probably on the wrong setting.
The end of the sender must be within 1/32" -1/16" of the gear teeth, but not touching the teeth. To adjust, stop engine, loosen the lock nut, and gently turn the sender clockwise until it touches the flywheel. Back off (counterclockwise) one turn, and secure with the locknut.
Rust buildup between the teeth can cause signal loss from the sender.
Dual stations: the sender will drive two tachometers. Simply connect "IGN" to "IGN", "GND" to "GND", etc. NOTE: mixing brands/ types (such as 2-wire/3-wire, see para graph 2 above) may cause problems.