Yes the tach should rise when cranking the engine and obviously anything in the crankshaft position sensor circuit including the sensor, connectors, wiring, etc. could cause a problem for it. So no, not just the sensor... anything in its circuit which includes the PCM. The CPS drives the PCM which derives the engine rpms from it and then drives the tach. Likely the sensor but....
Hmm, one of the first things I tried was swapping the cps out with a new one I got from Napa, which didn't help. I know the recommendation is to source Mopar sensors when possible, but I couldn't find any anywhere.
I'm suspicious of the PCM as well, but am trying to rule out other potential causes before I give Mark @Wranglerfix a call...