Check the wires coming out of the "nut". They like to chafe there and short. You jostling the wires makes them "not short" and when they settle back down to where they normally lay, it shorts back out.
Remove the sensor again, and clean the area where the wires come out of the "nut" and put a "hersheys kiss" of silicone, or cover both wires with some "liquid electrical tape". This may buy you some time... but I would be saving up for a new sensor.
Luckily for you, since you have a C-6 it could care less if the tach is working or not. So, at that is really happening is the gauge on the dash just doesn't work. The C-6 only "input" is the VRV (vacuum signal) on the side of the pump, the MPLS (Gear selector on the transmission) and the Kickdown. (If I missed something, someone will correct me shortly....) If you had an E4OD, it MUST have a good tach signal, among other signals to operate properly. No tach signal will send them into "limp mode" and will DESTROY your transmission in short order if driven that way....
