As far as I know, the only thing that could cause the tach to fail is the CPS as the signal from the tach comes directly from the CPS. That said, it could be a wiring issue too, maybe the wiring is messed up in that harness. I suppose it could be something with the Ignition Control Module as well since all the wires from the CPS go directly to the ICM, but I have never seen an ICM fail in that manner, I have seen a CPS fail that way.
The wiring that connects the CPS, Camshaft Position Sensor and the ICM is all one harness and down around where the CPS is a fair amount of heat from the block and such and that harness can become brittle and Im sure the connector itself can get that way as well, so there could be issues there.
Both spark and tach signals originate at the CPS then go to the ICM so I cant see the issue being anywhere else. The ICM does generate a Low and Medium resolution engine speed (tach signal) but I cannot tell from the schematic if the CPS is responsible for both, my suspicion is that it is not because two of the four CPS wires are for spark and tach, the other two are voltage and low reference, so that tach signal you are seeing is something from the transmission or one of those other engine speed signals.