It sounds mechanical. I wouldn't jump in and start replacing parts until you open up ignition switch assembly and see what's out of place. Jiggling the wheel most likely torques / applies pressure to the mechanism to keep the ignition tumbler from spinning.
https://www.pelicanparts.com/techarticles/Boxster_Tech/86-ELEC-Ignition_Switch/86-ELEC-Ignition_Switch.htm