I'm not sure I understand though,,,
You're not having a problem of any kind, you've just become aware of the intermittent movement of the Tach needle when cranking? - right?
You've heard "If it ain't broke, don't fix it?
Here's the thing, with an '01, if you have a Trans Temp Gauge in the Cluster it means you have the electrical revision that no longer has the CPS directly drive the Tach. If you don't, then you have the earlier electrics where the CPS does
drive the Tach, and give you some indication of the CPS's function. BUT, if the CPS wasn't functioning (and the lack of movement was
indicating that) there's No Way it would start! The PCM would actually be seeing "0" rpm and wouldn't fire the injectors.
The more typical CPS failure has to do with Temperature. As the engine gets hot, the CPS fails to send it's signal to the PCM, the engine stops and letting 15-20mins go by cools it enough to allow you to restart again.
I don't think you have a problem....