Put a VOM on the sensor with engine idling. You're looking for AC voltage from one sensor wire to another.
Resistance should read about 25k ohms.
Other diagnostics of the sensor require an IP gear chucked in a drill press...
If the sensor passes, check continuity of the sensor ground and signal wires. I don't know how to test the tach gauge itself, but have a functional spare I can send you.
Also, verify that the tach is getting 12v, ground, and signal through the three little pins that fit into the gauge cluster, which then goes through the printed PCB and into one of the plugs. Lots of points of failure in that whole assembly!
Btw, I can't remember if the TECA is upstream or downstream of the tach... I kinda lean towards a faulty sensor/wiring since neither the tach nor TECA appear to register RPMs