Follow the instructions at the link below. Also, if you have not removed the CPS or done anything else to cause it to be out of alignment since last start up, then its most likely not the sensor alignment. I had the same issue as you. Came to find out the wires on the harness side of the CPS connector were barely making a contact inside the back of the connector. Once I fixed this, the car has had no issues. There is a lot of heat on that side of the engine due to the exhaust being on the same side. Also you state that wiggling the wires caused it to start the last time. That would lead me to believe that there is a connector issue and not an alignment issue.
Also, when installing the CPS per the TSRM, the pick up will rotate as you push the CPS in place. Since the CAM and sensor both have helical gears, its unavoidable. The instructions account for this and so you do not (should not) compensate for the movement when installing. Once done, you can set the final timing as described in TSRM as well.
http://www.cygnusx1.net/Supra/Librar...ection=IG&P=21
Hope this helps......